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Volume growth and entropy for C^1 partially hyperbolic diffeomorphisms


We show that the metric entropy of a C^1 diffeomorphism with a dominated splitting and the dominating bundle uniformly expanding is bounded from above by the integrated volume growth of the dominating (expanding) bundle plus the maximal Lyapunov exponent from the dominated bundle multiplied by its dimension. We also discuss different types of volume growth that can be associated with an expanding foliation and relationships between them, specially when there exists a closed form non-degenerate on the foliation. Some consequences for partially hyperbolic diffeomorphisms are presented.

Autores: Saghin, R.

Journal: Discrete and Continuous Dynamical Systems – Series A

Journal Volume: 34

Journal Issue: 9

Journal Page: 3789-3801

Tipo de publicación: ISI

Fecha de publicación: 2014


DOI: 10.3934/dcds.2014.34.3789

URL de la publicación: https://arxiv.org/pdf/1202.1805v1.pdf

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