Periodic Point Data Detects Subdynamics in Entropy Rank One

Details Periodic Point Data Detects Subdynamics in Entropy Rank One Periodic Point Data Detects Subdynamics in Entropy Rank One

2006-02-28

arxiv.org/abs/math/0602665v1

Ergodic Theory and Dynamical Systems, 26, No. 6, 1913-1930 (2006)

Mathematics

Dynamical Systems

Scientific paper

10.1017/S014338570600054X

A framework for understanding the geometry of continuous actions of Z^d was developed by Boyle and Lind using the notion of expansive behavior along lower-dimensional subspaces. For algebraic Z^d-actions of entropy rank one, the expansive subdynamics is readily described in terms of Lyapunov exponents. Here we show that periodic point counts for elements of an entropy rank one action determine the expansive subdynamics. Moreover, the finer structure of the non-expansive set is visible in the topological and smooth structure of a set of functions associated to the periodic point data.

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