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Abstract: We continue the study of non-invertible topological dynamical systems withexpanding behavior. We introduce the class of {\em finite type} systems whichare characterized by the condition that, up to rescaling and uniformly boundeddistortion, there are only finitely many iterates. We show that subhyperbolicrational maps and finite subdivision rules in the sense of Cannon, Floyd,Kenyon, and Parry with bounded valence and mesh going to zero are of finitetype. In addition, we show that the limit dynamical system associated to aselfsimilar, contracting, recurrent, level-transitive group action in thesense of V. Nekrashevych is of finite type. The proof makes essential use ofan analog of the finiteness of cone types property enjoyed by hyperbolicgroups.



Author: Peter Haïssinsky LATP, Kevin M. Pilgrim

Source: https://arxiv.org/







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