Ergodic Theory and Dynamical Systems

Periodic point data detects subdynamics in entropy rank one

a1 School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK (e-mail:,

Article author query
miles r   [Google Scholar] 
ward t   [Google Scholar] 


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.

(Published Online November 14 2006)
(Received May 2 2006)
(Revised July 4 2006)