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Combinatorial models of expanding dynamical systems

Published online by Cambridge University Press:  24 January 2013

VOLODYMYR NEKRASHEVYCH
VOLODYMYR NEKRASHEVYCH*
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX, USA (email: nekrash@math.tamu.edu)
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Abstract

We prove homotopical rigidity of expanding dynamical systems, by showing that they are determined by a group-theoretic invariant. We use this to show that the Julia set of every expanding dynamical system is an inverse limit of simplicial complexes constructed by inductive cut-and-paste rules. Moreover, the cut-and-paste rules can be found algorithmically from the algebraic invariant.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 3 , June 2014 , pp. 938 - 985
Copyright
©2013 Cambridge University Press 

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