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Periodic point data detects subdynamics in entropy rank one

Miles, R.; Ward, T.

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Authors

R. Miles

T. Ward



Abstract

A framework for understanding the geometry of continuous actions of Z^d was developed by Boyle and Lind using the notion of expansive behaviour along lower-dimensional subspaces. For algebraic Zd-actions of entropy rank one, the expansive subdynamics are 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.

Citation

Miles, R., & Ward, T. (2006). Periodic point data detects subdynamics in entropy rank one. Ergodic Theory and Dynamical Systems, 26(6), 1913-1930. https://doi.org/10.1017/s014338570600054x

Journal Article Type Article
Publication Date Dec 1, 2006
Deposit Date Oct 12, 2012
Publicly Available Date Mar 29, 2024
Journal Ergodic Theory and Dynamical Systems
Print ISSN 0143-3857
Electronic ISSN 1469-4417
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 26
Issue 6
Pages 1913-1930
DOI https://doi.org/10.1017/s014338570600054x

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