2013/01/24 by VOLODYMYR NEKRASHEVYCH · 1 citation
paper · doi:10.1017/etds.2012.163
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.