Symbolic extensionsfor partially hyperbolic dynamical systems with 2-dimensional center bundle | Zendy

David Burguet | Zendy; Todd Fisher | Zendy

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Symbolic extensionsfor partially hyperbolic dynamical systems with 2-dimensional center bundle

Author(s) -

David Burguet,

Todd Fisher

Publication year - 2012

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2013.33.2253

Subject(s) - bundle , mathematics , hyperbolic set , pure mathematics , center (category theory) , entropy (arrow of time) , symbolic dynamics , extension (predicate logic) , dynamical systems theory , topological entropy , mathematical analysis , physics , computer science , quantum mechanics , chemistry , materials science , programming language , composite material , crystallography

We relate the symbolic extension entropy of a partially hyperbolic dynamical system to the entropy appearing at small scales in local center manifolds. In particular, we prove the existence of symbolic extensions for $\mathcal{C}^2$ partially hyperbolic diffeomorphisms with a $2$-dimensional center bundle. 200 words.

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