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Symbolic extensions and partially hyperbolic diffeomorphisms

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  • We show there are no symbolic extensions $C^1$-generically among diffeomorphisms containing nonhyperbolic robustly transitive sets with a center indecomposable bundle of dimension at least 2. Similarly, $C^1$-generically homoclinic classes with a center indecomposable bundle of dimension at least 2 that satisfy a technical assumption called index adaptation have no symbolic extensions.
    Mathematics Subject Classification: Primary: 37D30, 37C05, 37C20, 37B10.

    Citation:

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