On Mean Sensitive Tuples of Discrete Amenable Group Actions
Abstract Let (X, G) be a G-system which means that X is a perfect compact metric space and G is a countable discrete infinite amenable group continuously acting on X. In this paper, for an invariant measure %$\mu %$ of (X, G) and an integer n larger than 2, we introduce firstly the notions of %$\mu...
Ausführliche Beschreibung
Autor*in: |
Liu, Xiusheng [verfasserIn] |
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E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2022 |
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Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Übergeordnetes Werk: |
Enthalten in: Qualitative theory of dynamical systems - Basel : Birkhäuser, 1999, 22(2022), 1 vom: 29. Nov. |
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Übergeordnetes Werk: |
volume:22 ; year:2022 ; number:1 ; day:29 ; month:11 |
Links: |
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DOI / URN: |
10.1007/s12346-022-00701-y |
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Katalog-ID: |
SPR048763608 |
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520 | |a Abstract Let (X, G) be a G-system which means that X is a perfect compact metric space and G is a countable discrete infinite amenable group continuously acting on X. In this paper, for an invariant measure %$\mu %$ of (X, G) and an integer n larger than 2, we introduce firstly the notions of %$\mu %$-mean n-sensitive tuple with respect to a Følner sequence of G and %$\mu %$-n-sensitive in the mean tuple with respect to a Følner sequence of G and we show that if %$\mu %$ is ergodic, then every measure-theoretic n-entropy tuple for %$\mu %$ is a %$\mu %$-mean n-sensitive tuple with respect to each tempered Følner sequence of G. Then we introduce the concepts of mean n-sensitive tuple with respect to a Følner sequence of G and n-sensitive in the mean tuple with respect to a Følner sequence of G and we prove that each n-entropy tuple is a mean n-sensitive tuple with respect to each tempered Følner sequence of G for minimal G-systems. Finally, we introduce the notion of weakly n-sensitive in the mean tuple with respect to a Følner sequence of G and we obtain that the maximal mean equicontinuous factor with respect to a Følner sequence of G can be induced by the smallest invariant closed equivalence relation containing all weakly sensitive in the mean pairs with respect to the same Følner sequence of G. | ||
650 | 4 | |a Følner sequence |7 (dpeaa)DE-He213 | |
650 | 4 | |a Amenable group |7 (dpeaa)DE-He213 | |
650 | 4 | |a Mean sensitive tuple |7 (dpeaa)DE-He213 | |
650 | 4 | |a Weak sensitivity in the mean |7 (dpeaa)DE-He213 | |
700 | 1 | |a Yin, Jiandong |4 aut | |
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10.1007/s12346-022-00701-y doi (DE-627)SPR048763608 (SPR)s12346-022-00701-y-e DE-627 ger DE-627 rakwb eng Liu, Xiusheng verfasserin aut On Mean Sensitive Tuples of Discrete Amenable Group Actions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let (X, G) be a G-system which means that X is a perfect compact metric space and G is a countable discrete infinite amenable group continuously acting on X. In this paper, for an invariant measure %$\mu %$ of (X, G) and an integer n larger than 2, we introduce firstly the notions of %$\mu %$-mean n-sensitive tuple with respect to a Følner sequence of G and %$\mu %$-n-sensitive in the mean tuple with respect to a Følner sequence of G and we show that if %$\mu %$ is ergodic, then every measure-theoretic n-entropy tuple for %$\mu %$ is a %$\mu %$-mean n-sensitive tuple with respect to each tempered Følner sequence of G. Then we introduce the concepts of mean n-sensitive tuple with respect to a Følner sequence of G and n-sensitive in the mean tuple with respect to a Følner sequence of G and we prove that each n-entropy tuple is a mean n-sensitive tuple with respect to each tempered Følner sequence of G for minimal G-systems. Finally, we introduce the notion of weakly n-sensitive in the mean tuple with respect to a Følner sequence of G and we obtain that the maximal mean equicontinuous factor with respect to a Følner sequence of G can be induced by the smallest invariant closed equivalence relation containing all weakly sensitive in the mean pairs with respect to the same Følner sequence of G. Følner sequence (dpeaa)DE-He213 Amenable group (dpeaa)DE-He213 Mean sensitive tuple (dpeaa)DE-He213 Weak sensitivity in the mean (dpeaa)DE-He213 Yin, Jiandong aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 22(2022), 1 vom: 29. Nov. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:22 year:2022 number:1 day:29 month:11 https://dx.doi.org/10.1007/s12346-022-00701-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 22 2022 1 29 11 |
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10.1007/s12346-022-00701-y doi (DE-627)SPR048763608 (SPR)s12346-022-00701-y-e DE-627 ger DE-627 rakwb eng Liu, Xiusheng verfasserin aut On Mean Sensitive Tuples of Discrete Amenable Group Actions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let (X, G) be a G-system which means that X is a perfect compact metric space and G is a countable discrete infinite amenable group continuously acting on X. In this paper, for an invariant measure %$\mu %$ of (X, G) and an integer n larger than 2, we introduce firstly the notions of %$\mu %$-mean n-sensitive tuple with respect to a Følner sequence of G and %$\mu %$-n-sensitive in the mean tuple with respect to a Følner sequence of G and we show that if %$\mu %$ is ergodic, then every measure-theoretic n-entropy tuple for %$\mu %$ is a %$\mu %$-mean n-sensitive tuple with respect to each tempered Følner sequence of G. Then we introduce the concepts of mean n-sensitive tuple with respect to a Følner sequence of G and n-sensitive in the mean tuple with respect to a Følner sequence of G and we prove that each n-entropy tuple is a mean n-sensitive tuple with respect to each tempered Følner sequence of G for minimal G-systems. Finally, we introduce the notion of weakly n-sensitive in the mean tuple with respect to a Følner sequence of G and we obtain that the maximal mean equicontinuous factor with respect to a Følner sequence of G can be induced by the smallest invariant closed equivalence relation containing all weakly sensitive in the mean pairs with respect to the same Følner sequence of G. Følner sequence (dpeaa)DE-He213 Amenable group (dpeaa)DE-He213 Mean sensitive tuple (dpeaa)DE-He213 Weak sensitivity in the mean (dpeaa)DE-He213 Yin, Jiandong aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 22(2022), 1 vom: 29. Nov. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:22 year:2022 number:1 day:29 month:11 https://dx.doi.org/10.1007/s12346-022-00701-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 22 2022 1 29 11 |
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10.1007/s12346-022-00701-y doi (DE-627)SPR048763608 (SPR)s12346-022-00701-y-e DE-627 ger DE-627 rakwb eng Liu, Xiusheng verfasserin aut On Mean Sensitive Tuples of Discrete Amenable Group Actions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let (X, G) be a G-system which means that X is a perfect compact metric space and G is a countable discrete infinite amenable group continuously acting on X. In this paper, for an invariant measure %$\mu %$ of (X, G) and an integer n larger than 2, we introduce firstly the notions of %$\mu %$-mean n-sensitive tuple with respect to a Følner sequence of G and %$\mu %$-n-sensitive in the mean tuple with respect to a Følner sequence of G and we show that if %$\mu %$ is ergodic, then every measure-theoretic n-entropy tuple for %$\mu %$ is a %$\mu %$-mean n-sensitive tuple with respect to each tempered Følner sequence of G. Then we introduce the concepts of mean n-sensitive tuple with respect to a Følner sequence of G and n-sensitive in the mean tuple with respect to a Følner sequence of G and we prove that each n-entropy tuple is a mean n-sensitive tuple with respect to each tempered Følner sequence of G for minimal G-systems. Finally, we introduce the notion of weakly n-sensitive in the mean tuple with respect to a Følner sequence of G and we obtain that the maximal mean equicontinuous factor with respect to a Følner sequence of G can be induced by the smallest invariant closed equivalence relation containing all weakly sensitive in the mean pairs with respect to the same Følner sequence of G. Følner sequence (dpeaa)DE-He213 Amenable group (dpeaa)DE-He213 Mean sensitive tuple (dpeaa)DE-He213 Weak sensitivity in the mean (dpeaa)DE-He213 Yin, Jiandong aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 22(2022), 1 vom: 29. Nov. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:22 year:2022 number:1 day:29 month:11 https://dx.doi.org/10.1007/s12346-022-00701-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 22 2022 1 29 11 |
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10.1007/s12346-022-00701-y doi (DE-627)SPR048763608 (SPR)s12346-022-00701-y-e DE-627 ger DE-627 rakwb eng Liu, Xiusheng verfasserin aut On Mean Sensitive Tuples of Discrete Amenable Group Actions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let (X, G) be a G-system which means that X is a perfect compact metric space and G is a countable discrete infinite amenable group continuously acting on X. In this paper, for an invariant measure %$\mu %$ of (X, G) and an integer n larger than 2, we introduce firstly the notions of %$\mu %$-mean n-sensitive tuple with respect to a Følner sequence of G and %$\mu %$-n-sensitive in the mean tuple with respect to a Følner sequence of G and we show that if %$\mu %$ is ergodic, then every measure-theoretic n-entropy tuple for %$\mu %$ is a %$\mu %$-mean n-sensitive tuple with respect to each tempered Følner sequence of G. Then we introduce the concepts of mean n-sensitive tuple with respect to a Følner sequence of G and n-sensitive in the mean tuple with respect to a Følner sequence of G and we prove that each n-entropy tuple is a mean n-sensitive tuple with respect to each tempered Følner sequence of G for minimal G-systems. Finally, we introduce the notion of weakly n-sensitive in the mean tuple with respect to a Følner sequence of G and we obtain that the maximal mean equicontinuous factor with respect to a Følner sequence of G can be induced by the smallest invariant closed equivalence relation containing all weakly sensitive in the mean pairs with respect to the same Følner sequence of G. Følner sequence (dpeaa)DE-He213 Amenable group (dpeaa)DE-He213 Mean sensitive tuple (dpeaa)DE-He213 Weak sensitivity in the mean (dpeaa)DE-He213 Yin, Jiandong aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 22(2022), 1 vom: 29. Nov. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:22 year:2022 number:1 day:29 month:11 https://dx.doi.org/10.1007/s12346-022-00701-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 22 2022 1 29 11 |
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10.1007/s12346-022-00701-y doi (DE-627)SPR048763608 (SPR)s12346-022-00701-y-e DE-627 ger DE-627 rakwb eng Liu, Xiusheng verfasserin aut On Mean Sensitive Tuples of Discrete Amenable Group Actions 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Let (X, G) be a G-system which means that X is a perfect compact metric space and G is a countable discrete infinite amenable group continuously acting on X. In this paper, for an invariant measure %$\mu %$ of (X, G) and an integer n larger than 2, we introduce firstly the notions of %$\mu %$-mean n-sensitive tuple with respect to a Følner sequence of G and %$\mu %$-n-sensitive in the mean tuple with respect to a Følner sequence of G and we show that if %$\mu %$ is ergodic, then every measure-theoretic n-entropy tuple for %$\mu %$ is a %$\mu %$-mean n-sensitive tuple with respect to each tempered Følner sequence of G. Then we introduce the concepts of mean n-sensitive tuple with respect to a Følner sequence of G and n-sensitive in the mean tuple with respect to a Følner sequence of G and we prove that each n-entropy tuple is a mean n-sensitive tuple with respect to each tempered Følner sequence of G for minimal G-systems. Finally, we introduce the notion of weakly n-sensitive in the mean tuple with respect to a Følner sequence of G and we obtain that the maximal mean equicontinuous factor with respect to a Følner sequence of G can be induced by the smallest invariant closed equivalence relation containing all weakly sensitive in the mean pairs with respect to the same Følner sequence of G. Følner sequence (dpeaa)DE-He213 Amenable group (dpeaa)DE-He213 Mean sensitive tuple (dpeaa)DE-He213 Weak sensitivity in the mean (dpeaa)DE-He213 Yin, Jiandong aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 22(2022), 1 vom: 29. Nov. (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:22 year:2022 number:1 day:29 month:11 https://dx.doi.org/10.1007/s12346-022-00701-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 22 2022 1 29 11 |
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract Let (X, G) be a G-system which means that X is a perfect compact metric space and G is a countable discrete infinite amenable group continuously acting on X. 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on mean sensitive tuples of discrete amenable group actions |
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On Mean Sensitive Tuples of Discrete Amenable Group Actions |
abstract |
Abstract Let (X, G) be a G-system which means that X is a perfect compact metric space and G is a countable discrete infinite amenable group continuously acting on X. In this paper, for an invariant measure %$\mu %$ of (X, G) and an integer n larger than 2, we introduce firstly the notions of %$\mu %$-mean n-sensitive tuple with respect to a Følner sequence of G and %$\mu %$-n-sensitive in the mean tuple with respect to a Følner sequence of G and we show that if %$\mu %$ is ergodic, then every measure-theoretic n-entropy tuple for %$\mu %$ is a %$\mu %$-mean n-sensitive tuple with respect to each tempered Følner sequence of G. Then we introduce the concepts of mean n-sensitive tuple with respect to a Følner sequence of G and n-sensitive in the mean tuple with respect to a Følner sequence of G and we prove that each n-entropy tuple is a mean n-sensitive tuple with respect to each tempered Følner sequence of G for minimal G-systems. Finally, we introduce the notion of weakly n-sensitive in the mean tuple with respect to a Følner sequence of G and we obtain that the maximal mean equicontinuous factor with respect to a Følner sequence of G can be induced by the smallest invariant closed equivalence relation containing all weakly sensitive in the mean pairs with respect to the same Følner sequence of G. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
abstractGer |
Abstract Let (X, G) be a G-system which means that X is a perfect compact metric space and G is a countable discrete infinite amenable group continuously acting on X. In this paper, for an invariant measure %$\mu %$ of (X, G) and an integer n larger than 2, we introduce firstly the notions of %$\mu %$-mean n-sensitive tuple with respect to a Følner sequence of G and %$\mu %$-n-sensitive in the mean tuple with respect to a Følner sequence of G and we show that if %$\mu %$ is ergodic, then every measure-theoretic n-entropy tuple for %$\mu %$ is a %$\mu %$-mean n-sensitive tuple with respect to each tempered Følner sequence of G. Then we introduce the concepts of mean n-sensitive tuple with respect to a Følner sequence of G and n-sensitive in the mean tuple with respect to a Følner sequence of G and we prove that each n-entropy tuple is a mean n-sensitive tuple with respect to each tempered Følner sequence of G for minimal G-systems. Finally, we introduce the notion of weakly n-sensitive in the mean tuple with respect to a Følner sequence of G and we obtain that the maximal mean equicontinuous factor with respect to a Følner sequence of G can be induced by the smallest invariant closed equivalence relation containing all weakly sensitive in the mean pairs with respect to the same Følner sequence of G. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
abstract_unstemmed |
Abstract Let (X, G) be a G-system which means that X is a perfect compact metric space and G is a countable discrete infinite amenable group continuously acting on X. In this paper, for an invariant measure %$\mu %$ of (X, G) and an integer n larger than 2, we introduce firstly the notions of %$\mu %$-mean n-sensitive tuple with respect to a Følner sequence of G and %$\mu %$-n-sensitive in the mean tuple with respect to a Følner sequence of G and we show that if %$\mu %$ is ergodic, then every measure-theoretic n-entropy tuple for %$\mu %$ is a %$\mu %$-mean n-sensitive tuple with respect to each tempered Følner sequence of G. Then we introduce the concepts of mean n-sensitive tuple with respect to a Følner sequence of G and n-sensitive in the mean tuple with respect to a Følner sequence of G and we prove that each n-entropy tuple is a mean n-sensitive tuple with respect to each tempered Følner sequence of G for minimal G-systems. Finally, we introduce the notion of weakly n-sensitive in the mean tuple with respect to a Følner sequence of G and we obtain that the maximal mean equicontinuous factor with respect to a Følner sequence of G can be induced by the smallest invariant closed equivalence relation containing all weakly sensitive in the mean pairs with respect to the same Følner sequence of G. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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On Mean Sensitive Tuples of Discrete Amenable Group Actions |
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https://dx.doi.org/10.1007/s12346-022-00701-y |
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Yin, Jiandong |
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10.1007/s12346-022-00701-y |
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|
score |
7.3970747 |