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Article Dans Une Revue Groups, Geometry, and Dynamics Année : 2011

Finite type coarse expanding conformal dynamics

Peter Haïssinsky
Kevin Pilgrim
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We continue the study of non-invertible topological dynamical systems with expanding behavior. We introduce the class of {\em 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.
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Dates et versions

hal-00250031 , version 1 (08-02-2008)
hal-00250031 , version 2 (23-06-2011)



Peter Haïssinsky, Kevin Pilgrim. Finite type coarse expanding conformal dynamics. Groups, Geometry, and Dynamics, 2011, 5 (3), pp. 603-661. ⟨hal-00250031v2⟩
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