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A finiteness theorem for a dynamical class of entire functions

Published online by Cambridge University Press:  19 September 2008

Lisa R. Goldberg  and
Linda Keen
Lisa R. Goldberg
Affiliation:
C.U.N.Y., 33 West 42 Street, New York, NY 10036, USA
Linda Keen
Affiliation:
C.U.N.Y., 33 West 42 Street, New York, NY 10036, USA
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Abstract

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We define a class Σ of entire functions whose covering properties are similar to those of rational maps. The set Σ is closed under composition of functions, and we show that when regarded as dynamical systems of the plane, the elements of Σ share many properties with rational maps. In particular, they have finite dimensional spaces of quasiconformal deformations, and they contain no wandering domains in their stable sets.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 2 , June 1986 , pp. 183 - 192
Copyright
Copyright © Cambridge University Press 1986

References

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