# American Institute of Mathematical Sciences

April  2013, 33(4): 1333-1349. doi: 10.3934/dcds.2013.33.1333

## 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, Mexico 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, Germany

Received  September 2011 Revised  April 2012 Published  October 2012

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.
Citation: Carlos Cabrera, Peter Makienko, Peter Plaumann. Semigroup representations in holomorphic dynamics. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1333-1349. doi: 10.3934/dcds.2013.33.1333
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##### References:
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