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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: buzzi@math.polytechnique.fr)
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Abstract

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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.

Information

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