Entropy dimensions and a class of constructive examples

Sébastien Ferenczi; Kyewon Koh Park

doi:10.3934/dcds.2007.17.133

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2007, Volume 17, Issue 1: 133-141. Doi: 10.3934/dcds.2007.17.133

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Entropy dimensions and a class of constructive examples

Sébastien Ferenczi^1, and
Kyewon Koh Park^2,

1.
Institut de Mathématiques de Luminy, Case 907, 163 av. de Luminy, F13288 Marseille Cedex 9
2.
Department of Mathematics, Ajou University, Suwon 442-729

Received: February 2005

Revised: June 2006

Published: January 2007

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Abstract

Motivated by the study of actions of $\Z^{2}$ and more general groups, and their non-cocompact subgroup actions, we investigate entropy-type invariants for deterministic systems. In particular, we define a new isomorphism invariant, the entropy dimension, and look at its behaviour on examples. We also look at other natural notions suitable for processes.

Keywords:

Entropy,
Cutting and stacking.

Mathematics Subject Classification: Primary 37A35; Secondary 37A15.

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