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Symbolic extension entropy: \(C^r\) examples, products and flows. (English) Zbl 1110.37007

Summary: 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.

MSC:

37B10 Symbolic dynamics
37B40 Topological entropy
37C40 Smooth ergodic theory, invariant measures for smooth dynamical systems
37C05 Dynamical systems involving smooth mappings and diffeomorphisms
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