Regularity of Characteristic Exponents and Linear Response for Transfer Operator Cocycles
Abstract We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $$C^k$$ regularity with respect to coordinates and parameters, we show...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Sedro, Julien [verfasserIn] |
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Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer Berlin Heidelberg, 1965, 383(2021), 2 vom: 16. Feb., Seite 1243-1289 |
|---|---|
| Übergeordnetes Werk: |
volume:383 ; year:2021 ; number:2 ; day:16 ; month:02 ; pages:1243-1289 |
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| DOI / URN: |
10.1007/s00220-021-04019-9 |
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OLC2124728377 |
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| 520 | |a Abstract We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $$C^k$$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $$C^{k-1}$$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters. | ||
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10.1007/s00220-021-04019-9 doi (DE-627)OLC2124728377 (DE-He213)s00220-021-04019-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Sedro, Julien verfasserin (orcid)0000-0001-9208-8406 aut Regularity of Characteristic Exponents and Linear Response for Transfer Operator Cocycles 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $$C^k$$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $$C^{k-1}$$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters. Rugh, Hans Henrik aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 383(2021), 2 vom: 16. Feb., Seite 1243-1289 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:383 year:2021 number:2 day:16 month:02 pages:1243-1289 https://doi.org/10.1007/s00220-021-04019-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4277 AR 383 2021 2 16 02 1243-1289 |
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10.1007/s00220-021-04019-9 doi (DE-627)OLC2124728377 (DE-He213)s00220-021-04019-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Sedro, Julien verfasserin (orcid)0000-0001-9208-8406 aut Regularity of Characteristic Exponents and Linear Response for Transfer Operator Cocycles 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $$C^k$$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $$C^{k-1}$$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters. Rugh, Hans Henrik aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 383(2021), 2 vom: 16. Feb., Seite 1243-1289 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:383 year:2021 number:2 day:16 month:02 pages:1243-1289 https://doi.org/10.1007/s00220-021-04019-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4277 AR 383 2021 2 16 02 1243-1289 |
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10.1007/s00220-021-04019-9 doi (DE-627)OLC2124728377 (DE-He213)s00220-021-04019-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Sedro, Julien verfasserin (orcid)0000-0001-9208-8406 aut Regularity of Characteristic Exponents and Linear Response for Transfer Operator Cocycles 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $$C^k$$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $$C^{k-1}$$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters. Rugh, Hans Henrik aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 383(2021), 2 vom: 16. Feb., Seite 1243-1289 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:383 year:2021 number:2 day:16 month:02 pages:1243-1289 https://doi.org/10.1007/s00220-021-04019-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4277 AR 383 2021 2 16 02 1243-1289 |
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10.1007/s00220-021-04019-9 doi (DE-627)OLC2124728377 (DE-He213)s00220-021-04019-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Sedro, Julien verfasserin (orcid)0000-0001-9208-8406 aut Regularity of Characteristic Exponents and Linear Response for Transfer Operator Cocycles 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $$C^k$$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $$C^{k-1}$$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters. Rugh, Hans Henrik aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 383(2021), 2 vom: 16. Feb., Seite 1243-1289 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:383 year:2021 number:2 day:16 month:02 pages:1243-1289 https://doi.org/10.1007/s00220-021-04019-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4277 AR 383 2021 2 16 02 1243-1289 |
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10.1007/s00220-021-04019-9 doi (DE-627)OLC2124728377 (DE-He213)s00220-021-04019-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Sedro, Julien verfasserin (orcid)0000-0001-9208-8406 aut Regularity of Characteristic Exponents and Linear Response for Transfer Operator Cocycles 2021 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 Abstract We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $$C^k$$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $$C^{k-1}$$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters. Rugh, Hans Henrik aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 383(2021), 2 vom: 16. Feb., Seite 1243-1289 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:383 year:2021 number:2 day:16 month:02 pages:1243-1289 https://doi.org/10.1007/s00220-021-04019-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_70 GBV_ILN_2018 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4277 AR 383 2021 2 16 02 1243-1289 |
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Abstract We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $$C^k$$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $$C^{k-1}$$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters. © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 |
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Abstract We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $$C^k$$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $$C^{k-1}$$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters. © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 |
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Abstract We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. Assuming $$C^k$$ regularity with respect to coordinates and parameters, we show that when the sequence is picked within a certain uniform family the top characteristic exponent and generator of top Oseledets space of the cocycle are $$C^{k-1}$$ in parameters. As applications, we obtain a linear response formula for the equivariant measure associated with random products of uniformly expanding maps, and we study the regularity of the Hausdorff dimension of a repeller associated with random compositions of one-dimensional cookie-cutters. © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2124728377</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505092457.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230505s2021 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00220-021-04019-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2124728377</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00220-021-04019-9-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">530</subfield><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Sedro, Julien</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0001-9208-8406</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Regularity of Characteristic Exponents and Linear Response for Transfer Operator Cocycles</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract We consider cocycles obtained by composing sequences of transfer operators with positive weights, associated with uniformly expanding maps (possibly having countably many branches) and depending upon parameters. 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