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...
| Authors: | ; ; |
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| Format: | Article |
| Publication date: | 2010 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:52297 |
| Online Access: | https://ddd.uab.cat/record/52297 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_54110_06 |
| Access Level: | Open access |
| Keyword: | Julia sets Polynomial-like maps Combinatorial dynamics |
| Summary: | 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. |
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