# name
Deformations of entire functions with Baker domains

# metadata.dc.description.abstract[].value
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 $f$.

# metadata.dc.publisher[].value
American Institute of Mathematical Sciences (AIMS)

# metadata.dc.relation.ispartof[].value
Discrete and Continuous Dynamical Systems-Series A, 2006, vol. 15, num. 2, p. 379-394

# metadata.dc.rights[].value
(c) American Institute of Mathematical Sciences (AIMS), 2006

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Deformations of entire functions with Baker domains