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 (06). pp. 1913-1930. ISSN 0143-3857

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A framework for understanding the geometry of continuous actions of Zd 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.

Item Type: Article
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Vishal Gautam
Date Deposited: 18 Mar 2011 14:48
Last Modified: 13 Feb 2023 12:30
DOI: 10.1017/S014338570600054X

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