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http://hdl.handle.net/2445/164126
Title: | Deformations of entire functions with Baker domains |
Author: | Fagella Rabionet, Núria Henriksen, Christian |
Keywords: | Sistemes dinàmics complexos Funcions de variables complexes Complex dynamical systems Functions of complex variables |
Issue Date: | 2006 |
Publisher: | American Institute of Mathematical Sciences (AIMS) |
Abstract: | We consider entire transcendental functions $f$ with an invariant (or periodic) Baker domain $U$. First, we classify these domains into three types (hyperbolic, simply parabolic and doubly parabolic) according to the surface they induce when we take the quotient by the dynamics. Second, we study the space of quasiconformal deformations of an entire map with such a Baker domain by studying its Teichmuüller space. More precisely, we show that the dimension of this set is infinite if the Baker domain is hyperbolic or simply parabolic, and from this we deduce that the quasiconformal deformation space of $f$ is infinite dimensional. Finally, we prove that the function $f(z)=z+e^{-z}$, which possesses infinitely many invariant Baker domains, is rigid, i.e., any quasiconformal deformation of $f$ is affinely conjugate to $f$. |
Note: | Reproducció del document publicat a: https://doi.org/10.3934/dcds.2006.15.379 |
It is part of: | Discrete and Continuous Dynamical Systems-Series A, 2006, vol. 15, num. 2, p. 379-394 |
URI: | http://hdl.handle.net/2445/164126 |
Related resource: | https://doi.org/10.3934/dcds.2006.15.379 |
ISSN: | 1078-0947 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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