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Periodic point data detects subdynamics in entropy rank one.

Miles, R. and Ward, T. (2006) 'Periodic point data detects subdynamics in entropy rank one.', Ergodic theory and dynamical systems., 26 (6). pp. 1913-1930.

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.

Item Type:Article
Full text:PDF - Accepted Version (136Kb)
Full text:PDF - Published Version (233Kb)
Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1017/S014338570600054X
Publisher statement:© Copyright Cambridge University Press 2006. This paper has been published in a revised form subsequent to editorial input by Cambridge University Press in "Ergodic theory and dynamical systems" (26: 6 (2006) 1913-1930) http://journals.cambridge.org/action/displayJournal?jid=ETS
Record Created:12 Oct 2012 10:50
Last Modified:25 Oct 2012 12:04

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