We show that the metric entropy of a C1 diffeomorphism with a dominated splitting and with 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.
|Number of pages||13|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|State||Published - 1 Jan 2014|
- Partially hyperbolic diffeomorphisms
- Volume growth