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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 $f$.
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It is part of: Discrete and Continuous Dynamical Systems-Series A, 2006, vol. 15, num. 2, p. 379-394
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ISSN: 1078-0947
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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