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June  2006, 16(2): 329-341. doi: 10.3934/dcds.2006.16.329

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, United States
2. 

Institute of Mathematics, Technical University, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland

Received  March 2005 Published  July 2006

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.
Keywords: entropy, sex entropy, residual entropy, superenvelope..
Mathematics Subject Classification: Primary: 37B10; Secondary: 37B40, 37C40, 37C45,37C99, 37D3.
Citation: Mike Boyle, Tomasz Downarowicz. Symbolic extension entropy: $c^r$ examples, products and flows. Discrete and Continuous Dynamical Systems, 2006, 16 (2) : 329-341. doi: 10.3934/dcds.2006.16.329
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