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Combinatorial models of expanding dynamical systems.(English)Zbl 1350.37034

Summary: 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.

MSC:

37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.)
37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems
37B15 Dynamical aspects of cellular automata
37F15 Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems
37F20 Combinatorics and topology in relation with holomorphic dynamical systems
20M35 Semigroups in automata theory, linguistics, etc.
37F50 Small divisors, rotation domains and linearization in holomorphic dynamics

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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