Periodic point data detects subdynamics in entropy rank one

Richard Miles, Thomas Ward

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1913-1930
Number of pages18
JournalErgodic Theory and Dynamical Systems
Issue number06
Publication statusPublished - 2006

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