Semigroup representations in holomorphic dynamics

Carlos Cabrera; Peter Makienko; Peter Plaumann

doi:10.3934/dcds.2013.33.1333

Article Contents

2013, Volume 33, Issue 4: 1333-1349. Doi: 10.3934/dcds.2013.33.1333

This issue Previous Article Dynamics of continued fractions and kneading sequences of unimodal maps Next Article Entropy of endomorphisms of Lie groups

Semigroup representations in holomorphic dynamics

1.
Instituto de Matemáticas., Unidad Cuernavaca. UNAM, Av. Universidad s/n. Col. Lomas de Chamilpa, C. P. 62210, Cuernavaca, Morelos
2.
Instituto de Matemáticas, Unidad Cuernavaca. UNAM, Av. Universidad s/n. Col. Lomas de Chamilpa, C.P. 62210, Cuernavaca, Morelos
3.
Mathematisches Institut, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen

Received: August 31, 2011

Revised: March 31, 2012

Published: March 2013

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Abstract

We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. We show, with some examples, that representation theory of semigroups is related to usual constructions in holomorphic dynamics. The main tool for our discussion is a theorem due to Schreier. We extend this theorem, and our results in semigroups, to the setting of correspondences and holomorphic correspondences.

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Mathematics Subject Classification: 37F05, 37F10, 20M30.

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