Symbolic extension entropy: $c^r$ examples, products and flows

Mike Boyle; Tomasz Downarowicz

doi:10.3934/dcds.2006.16.329

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2006, Volume 16, Issue 2: 329-341. Doi: 10.3934/dcds.2006.16.329

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Symbolic extension entropy: $c^r$ examples, products and flows

Mike Boyle^1, and
Tomasz Downarowicz^2,

1.
Department of Mathematics, University of Maryland, College Park, MD 20742-4015
2.
Institute of Mathematics, Technical University, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław

Received: February 28, 2005

Published: March 2006

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Abstract

Adapting techniques of Misiurewicz, for $1\leq r < \infty$ we give an explicit construction of $C^r$ maps with positive residual entropy. We also establish the behavior of symbolic extension entropy with respect to joinings, fiber products, products, powers and flows.

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Mathematics Subject Classification: Primary: 37B10; Secondary: 37B40, 37C40, 37C45,37C99, 37D35.

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