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Topology and growth of a special class of holomorphic self-maps of ℂ*

Published online by Cambridge University Press:  19 September 2008

Linda Keen
Linda Keen
Affiliation:
Department of Mathematics, Lehman College, Bronx, New York, 10468, USA
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Abstract

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It is a general problem to find appropriate sets of moduli for families of functions that generate dynamical systems. In this paper we solve this problem for a specific family of holomorphic self-maps of ℂ* defined by

The main theorem states that any function topologically conjugate to a member of ℱ is holomorphically conjugate to some member of the family. It follows that the coefficients of the polynomials P(z) and Q(z) are a suitable set of moduli for the families of dynamical systems generated by these functions.

The moduli spaces of functions in ℱ are easy to study computationally and have been studied by many authors. (See references in the text.)

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 9 , Issue 2 , June 1989 , pp. 321 - 328
Copyright
Copyright © Cambridge University Press 1989

References

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