# American Institute of Mathematical Sciences

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

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

 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.
Citation: Mike Boyle, Tomasz Downarowicz. Symbolic extension entropy: $c^r$ examples, products and flows. Discrete & Continuous Dynamical Systems, 2006, 16 (2) : 329-341. doi: 10.3934/dcds.2006.16.329
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