The Parameter Planes of $ λz^{m} $ exp(z) for m ≥ 2*
Abstract We consider the families of entire transcendental maps given by Fλ,m (z) = $ λz^{m} $ exp(z), where m ≥ 2. All functions Fλ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the crit...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Fagella, Núria [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2007 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag 2007 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Berlin : Springer, 1965, 273(2007), 3 vom: 31. Mai, Seite 755-783 |
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| Übergeordnetes Werk: |
volume:273 ; year:2007 ; number:3 ; day:31 ; month:05 ; pages:755-783 |
| Links: |
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| DOI / URN: |
10.1007/s00220-007-0265-8 |
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SPR00233982X |
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| 100 | 1 | |a Fagella, Núria |e verfasserin |4 aut | |
| 245 | 1 | 4 | |a The Parameter Planes of $ λz^{m} $ exp(z) for m ≥ 2* |
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| 520 | |a Abstract We consider the families of entire transcendental maps given by Fλ,m (z) = $ λz^{m} $ exp(z), where m ≥ 2. All functions Fλ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of %$\mathbb {C}^*%$ which serve as a model for Fλ,m, in the sense that they are related by means of quasiconformal surgery to Fλ,m. | ||
| 650 | 4 | |a Entire Function |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Quasiconformal Mapping |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Parameter Plane |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Capture Zone |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Dynamical Plane |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Garijo, Antonio |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Communications in mathematical physics |d Berlin : Springer, 1965 |g 273(2007), 3 vom: 31. Mai, Seite 755-783 |w (DE-627)253721628 |w (DE-600)1458931-X |x 1432-0916 |7 nnns |
| 773 | 1 | 8 | |g volume:273 |g year:2007 |g number:3 |g day:31 |g month:05 |g pages:755-783 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s00220-007-0265-8 |z lizenzpflichtig |3 Volltext |
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10.1007/s00220-007-0265-8 doi (DE-627)SPR00233982X (SPR)s00220-007-0265-8-e DE-627 ger DE-627 rakwb eng Fagella, Núria verfasserin aut The Parameter Planes of $ λz^{m} $ exp(z) for m ≥ 2* 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2007 Abstract We consider the families of entire transcendental maps given by Fλ,m (z) = $ λz^{m} $ exp(z), where m ≥ 2. All functions Fλ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of %$\mathbb {C}^*%$ which serve as a model for Fλ,m, in the sense that they are related by means of quasiconformal surgery to Fλ,m. Entire Function (dpeaa)DE-He213 Quasiconformal Mapping (dpeaa)DE-He213 Parameter Plane (dpeaa)DE-He213 Capture Zone (dpeaa)DE-He213 Dynamical Plane (dpeaa)DE-He213 Garijo, Antonio aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 273(2007), 3 vom: 31. Mai, Seite 755-783 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:273 year:2007 number:3 day:31 month:05 pages:755-783 https://dx.doi.org/10.1007/s00220-007-0265-8 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 273 2007 3 31 05 755-783 |
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10.1007/s00220-007-0265-8 doi (DE-627)SPR00233982X (SPR)s00220-007-0265-8-e DE-627 ger DE-627 rakwb eng Fagella, Núria verfasserin aut The Parameter Planes of $ λz^{m} $ exp(z) for m ≥ 2* 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2007 Abstract We consider the families of entire transcendental maps given by Fλ,m (z) = $ λz^{m} $ exp(z), where m ≥ 2. All functions Fλ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of %$\mathbb {C}^*%$ which serve as a model for Fλ,m, in the sense that they are related by means of quasiconformal surgery to Fλ,m. Entire Function (dpeaa)DE-He213 Quasiconformal Mapping (dpeaa)DE-He213 Parameter Plane (dpeaa)DE-He213 Capture Zone (dpeaa)DE-He213 Dynamical Plane (dpeaa)DE-He213 Garijo, Antonio aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 273(2007), 3 vom: 31. Mai, Seite 755-783 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:273 year:2007 number:3 day:31 month:05 pages:755-783 https://dx.doi.org/10.1007/s00220-007-0265-8 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 273 2007 3 31 05 755-783 |
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10.1007/s00220-007-0265-8 doi (DE-627)SPR00233982X (SPR)s00220-007-0265-8-e DE-627 ger DE-627 rakwb eng Fagella, Núria verfasserin aut The Parameter Planes of $ λz^{m} $ exp(z) for m ≥ 2* 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2007 Abstract We consider the families of entire transcendental maps given by Fλ,m (z) = $ λz^{m} $ exp(z), where m ≥ 2. All functions Fλ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of %$\mathbb {C}^*%$ which serve as a model for Fλ,m, in the sense that they are related by means of quasiconformal surgery to Fλ,m. Entire Function (dpeaa)DE-He213 Quasiconformal Mapping (dpeaa)DE-He213 Parameter Plane (dpeaa)DE-He213 Capture Zone (dpeaa)DE-He213 Dynamical Plane (dpeaa)DE-He213 Garijo, Antonio aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 273(2007), 3 vom: 31. Mai, Seite 755-783 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:273 year:2007 number:3 day:31 month:05 pages:755-783 https://dx.doi.org/10.1007/s00220-007-0265-8 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 273 2007 3 31 05 755-783 |
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10.1007/s00220-007-0265-8 doi (DE-627)SPR00233982X (SPR)s00220-007-0265-8-e DE-627 ger DE-627 rakwb eng Fagella, Núria verfasserin aut The Parameter Planes of $ λz^{m} $ exp(z) for m ≥ 2* 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2007 Abstract We consider the families of entire transcendental maps given by Fλ,m (z) = $ λz^{m} $ exp(z), where m ≥ 2. All functions Fλ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of %$\mathbb {C}^*%$ which serve as a model for Fλ,m, in the sense that they are related by means of quasiconformal surgery to Fλ,m. Entire Function (dpeaa)DE-He213 Quasiconformal Mapping (dpeaa)DE-He213 Parameter Plane (dpeaa)DE-He213 Capture Zone (dpeaa)DE-He213 Dynamical Plane (dpeaa)DE-He213 Garijo, Antonio aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 273(2007), 3 vom: 31. Mai, Seite 755-783 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:273 year:2007 number:3 day:31 month:05 pages:755-783 https://dx.doi.org/10.1007/s00220-007-0265-8 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 273 2007 3 31 05 755-783 |
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10.1007/s00220-007-0265-8 doi (DE-627)SPR00233982X (SPR)s00220-007-0265-8-e DE-627 ger DE-627 rakwb eng Fagella, Núria verfasserin aut The Parameter Planes of $ λz^{m} $ exp(z) for m ≥ 2* 2007 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2007 Abstract We consider the families of entire transcendental maps given by Fλ,m (z) = $ λz^{m} $ exp(z), where m ≥ 2. All functions Fλ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of %$\mathbb {C}^*%$ which serve as a model for Fλ,m, in the sense that they are related by means of quasiconformal surgery to Fλ,m. Entire Function (dpeaa)DE-He213 Quasiconformal Mapping (dpeaa)DE-He213 Parameter Plane (dpeaa)DE-He213 Capture Zone (dpeaa)DE-He213 Dynamical Plane (dpeaa)DE-He213 Garijo, Antonio aut Enthalten in Communications in mathematical physics Berlin : Springer, 1965 273(2007), 3 vom: 31. Mai, Seite 755-783 (DE-627)253721628 (DE-600)1458931-X 1432-0916 nnns volume:273 year:2007 number:3 day:31 month:05 pages:755-783 https://dx.doi.org/10.1007/s00220-007-0265-8 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 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_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 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_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 273 2007 3 31 05 755-783 |
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Enthalten in Communications in mathematical physics 273(2007), 3 vom: 31. Mai, Seite 755-783 volume:273 year:2007 number:3 day:31 month:05 pages:755-783 |
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Enthalten in Communications in mathematical physics 273(2007), 3 vom: 31. Mai, Seite 755-783 volume:273 year:2007 number:3 day:31 month:05 pages:755-783 |
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Fagella, Núria @@aut@@ Garijo, Antonio @@aut@@ |
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All functions Fλ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A*(0) is a quasidisk. 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Fagella, Núria |
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Fagella, Núria misc Entire Function misc Quasiconformal Mapping misc Parameter Plane misc Capture Zone misc Dynamical Plane The Parameter Planes of $ λz^{m} $ exp(z) for m ≥ 2* |
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The Parameter Planes of $ λz^{m} $ exp(z) for m ≥ 2* Entire Function (dpeaa)DE-He213 Quasiconformal Mapping (dpeaa)DE-He213 Parameter Plane (dpeaa)DE-He213 Capture Zone (dpeaa)DE-He213 Dynamical Plane (dpeaa)DE-He213 |
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parameter planes of $ λz^{m} $ exp(z) for m ≥ 2* |
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The Parameter Planes of $ λz^{m} $ exp(z) for m ≥ 2* |
| abstract |
Abstract We consider the families of entire transcendental maps given by Fλ,m (z) = $ λz^{m} $ exp(z), where m ≥ 2. All functions Fλ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of %$\mathbb {C}^*%$ which serve as a model for Fλ,m, in the sense that they are related by means of quasiconformal surgery to Fλ,m. © Springer-Verlag 2007 |
| abstractGer |
Abstract We consider the families of entire transcendental maps given by Fλ,m (z) = $ λz^{m} $ exp(z), where m ≥ 2. All functions Fλ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of %$\mathbb {C}^*%$ which serve as a model for Fλ,m, in the sense that they are related by means of quasiconformal surgery to Fλ,m. © Springer-Verlag 2007 |
| abstract_unstemmed |
Abstract We consider the families of entire transcendental maps given by Fλ,m (z) = $ λz^{m} $ exp(z), where m ≥ 2. All functions Fλ,m have a superattracting fixed point at z = 0, and a critical point at z = −m. In the parameter planes we focus on the capture zones, i.e., λ values for which the critical point belongs to the basin of attraction of z = 0, denoted by A(0). In particular, we study the main capture zone (parameter values for which the critical point lies in the immediate basin, A*(0)) and prove that is bounded, connected and simply connected. All other capture zones are unbounded and simply connected. For each parameter λ in the main capture zone, A(0) consists of a single connected component with non-locally connected boundary. For all remaining values of λ, A*(0) is a quasidisk. On a different approach, we introduce some families of holomorphic maps of %$\mathbb {C}^*%$ which serve as a model for Fλ,m, in the sense that they are related by means of quasiconformal surgery to Fλ,m. © Springer-Verlag 2007 |
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| title_short |
The Parameter Planes of $ λz^{m} $ exp(z) for m ≥ 2* |
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https://dx.doi.org/10.1007/s00220-007-0265-8 |
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Garijo, Antonio |
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10.1007/s00220-007-0265-8 |
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2024-07-04T02:40:17.416Z |
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| score |
7.402439 |