Hostname: page-component-cb9f654ff-r5d9c Total loading time: 0 Render date: 2025-08-18T12:05:45.736Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodic point data detects subdynamics in entropy rank one

Published online by Cambridge University Press:  14 November 2006

RICHARD MILES  and
THOMAS WARD
RICHARD MILES
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK (e-mail: r.miles@uea.ac.uk, t.ward@uea.ac.uk)
THOMAS WARD
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK (e-mail: r.miles@uea.ac.uk, t.ward@uea.ac.uk)
Get access Rights & Permissions [Opens in a new window]

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.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 6 , December 2006 , pp. 1913 - 1930
Copyright
2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable