Periodic point data detects subdynamics in entropy rank one

Miles, R.; Ward, T.

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: Oct 24, 2012
• 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