Periodic point data detects subdynamics in entropy rank one

MILES, Richard and WARD, Thomas (2006). Periodic point data detects subdynamics in entropy rank one. Ergodic Theory and Dynamical Systems, 26 (6), 1913-1930.

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Abstract

A framework for understanding the geometry of continuous actions of $\mathbb Z^d$ was developed by Boyle and Lind using the notion of expansive behaviour along lower-dimensional subspaces. For algebraic $\mathbb Z^d$-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.

Item Type:	Article
Departments - Does NOT include content added after October 2018:	Faculty of Social Sciences and Humanities > Department of Teacher Education
Identification Number:	https://doi.org/10.1017/5014338570600054x
Page Range:	1913-1930
Depositing User:	Richard Miles
Date Deposited:	26 Jan 2018 13:27
Last Modified:	18 Mar 2021 16:30
URI:	https://shura.shu.ac.uk/id/eprint/17238

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