Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-27T04:48:51.309Z Has data issue: false hasContentIssue false
  • English
  • Français

Piecewise isometries have zero topological entropy

Published online by Cambridge University Press:  02 October 2001

JÉRÔME BUZZI
JÉRÔME BUZZI
Affiliation:
Centre de Mathématique de l'Ecole Polytechnique, UMR 7640 du CNRS, 91128 Palaiseau cedex, France (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that piecewise isometries, i.e. non-necessarily invertible maps defined on a finite union of polytopes and coinciding with an isometry on the interior of each polytope, have zero topological entropy in any dimension. This had been conjectured by a number of authors. The proof is by an induction on the dimension and uses a device (the differential of a piecewise linear map) introduced by M. Tsujii.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 5 , October 2001 , pp. 1371 - 1377
Copyright
2001 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.)