JournalsggdVol. 5, No. 3pp. 603–661

Finite type coarse expanding conformal dynamics

  • Peter Haïssinsky

    Université Paul Sabatier, Toulouse, France
  • Constantin Dorin Dumitrașcu

    Adrian College, USA
Finite type coarse expanding conformal dynamics cover
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Abstract

We continue the study of noninvertible topological dynamical systems with expanding behavior. We introduce the class of finite type systems which are characterized by the condition that, up to rescaling and uniformly bounded distortion, there are only finitely many iterates. We show that subhyperbolic rational maps and finite subdivision rules (in the sense of Cannon, Floyd, Kenyon, and Parry) with bounded valence and mesh going to zero are of finite type. In addition, we show that the limit dynamical system associated to a selfsimilar, contracting, recurrent, level-transitive group action (in the sense of V. Nekrashevych) is of finite type. The proof makes essential use of an analog of the finiteness of cone types property enjoyed by hyperbolic groups.

Cite this article

Peter Haïssinsky, Constantin Dorin Dumitrașcu, Finite type coarse expanding conformal dynamics. Groups Geom. Dyn. 5 (2011), no. 3, pp. 603–661

DOI 10.4171/GGD/141