Joining polynomial and exponential combinatorics for some entire maps
We consider families of entire transcendental maps given by Fλ,m (z) = λzm exp (z) where m ≥ 2. All these maps have a superattracting fixed point at z = 0 and a free critical point at z = -m. In parameter planes we focus on the capture zones, i.e., we consider λ values for which the free critical po...
| Autores: | ; ; |
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| Tipo de documento: | Artículo |
| Fecha de publicación: | 2010 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Lenguaje: | Inglés |
| OAI Identifier: | oai:ddd.uab.cat:52297 |
| Acceso en línea: | https://ddd.uab.cat/record/52297 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_54110_06 |
| Nivel de acceso: | Acceso abierto |
| Palabra clave: | Julia sets Polynomial-like maps Combinatorial dynamics |
| _version_ | 1878740155581333504 |
|---|---|
| author | Garijo, Antoni|||0000-0002-1503-7514 |
| author2 | Jarque i Ribera, Xavier|||0000-0002-6576-9780 Moreno Rocha, Mónica|||0000-0003-3816-4425 |
| author2_role | author author |
| author_browse | Garijo, Antoni|||0000-0002-1503-7514 Jarque i Ribera, Xavier|||0000-0002-6576-9780 Moreno Rocha, Mónica|||0000-0003-3816-4425 |
| author_facet | Garijo, Antoni|||0000-0002-1503-7514 Jarque i Ribera, Xavier|||0000-0002-6576-9780 Moreno Rocha, Mónica|||0000-0003-3816-4425 |
| author_role | author |
| collection | Dipòsit Digital de Documents de la UAB |
| description | We consider families of entire transcendental maps given by Fλ,m (z) = λzm exp (z) where m ≥ 2. All these maps have a superattracting fixed point at z = 0 and a free critical point at z = -m. In parameter planes we focus on the capture zones, i.e., we consider λ values for which the free critical point belongs to the basin of attraction of z = 0. We explain the connection between the dynamics near zero and the dynamics near infinity at the boundary of the immediate basin of attraction of the origin, thus, joining together exponential and polynomial behaviors in the same dynamical plane. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ES_ce3a923c9af154353d7eaaf4c1eece3c |
| institution | Universitat Autònoma de Barcelona |
| instname_str | Universitat Autònoma de Barcelona |
| language | eng |
| network_acronym_str | ES |
| network_name_str | España |
| oai_identifier_str | oai:ddd.uab.cat:52297 |
| publishDate | 2010 |
| publishDateSort | 2010 |
| reponame_str | Dipòsit Digital de Documents de la UAB |
| spelling | Joining polynomial and exponential combinatorics for some entire maps Garijo, Antoni|||0000-0002-1503-7514 Jarque i Ribera, Xavier|||0000-0002-6576-9780 Moreno Rocha, Mónica|||0000-0003-3816-4425 Julia sets Polynomial-like maps Combinatorial dynamics We consider families of entire transcendental maps given by Fλ,m (z) = λzm exp (z) where m ≥ 2. All these maps have a superattracting fixed point at z = 0 and a free critical point at z = -m. In parameter planes we focus on the capture zones, i.e., we consider λ values for which the free critical point belongs to the basin of attraction of z = 0. We explain the connection between the dynamics near zero and the dynamics near infinity at the boundary of the immediate basin of attraction of the origin, thus, joining together exponential and polynomial behaviors in the same dynamical plane. https://ddd.uab.cat/record/52297 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_54110_06 |
| spellingShingle | Joining polynomial and exponential combinatorics for some entire maps Garijo, Antoni|||0000-0002-1503-7514 Julia sets Polynomial-like maps Combinatorial dynamics |
| title | Joining polynomial and exponential combinatorics for some entire maps |
| title_full | Joining polynomial and exponential combinatorics for some entire maps |
| title_fullStr | Joining polynomial and exponential combinatorics for some entire maps |
| title_full_unstemmed | Joining polynomial and exponential combinatorics for some entire maps |
| title_short | Joining polynomial and exponential combinatorics for some entire maps |
| title_sort | Joining polynomial and exponential combinatorics for some entire maps |
| topic | Julia sets Polynomial-like maps Combinatorial dynamics |
| topic_facet | Julia sets Polynomial-like maps Combinatorial dynamics |
| url | https://ddd.uab.cat/record/52297 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_54110_06 |