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articleNo Access
Random entropy expansiveness for diffeomorphisms with dominated splittings
- Zeya Mi
Stochastics and Dynamics25 Jul 2019
Preview Abstract
We study the local entropy of typical infinite Bowen balls in random dynamical systems, and show the random entropy expansiveness for $C^{1}$ partially hyperbolic diffeomorphisms with multi one-dimensional centers. Moreover, we consider $C^{1}$ diffeomorphism $f$ with dominated splitting $T M = E^{c u} \oplus E_{1}^{c} \oplus \dots \oplus E_{k}^{c} \oplus E^{c s}$ such that $dim E_{i}^{c} = 1$ for every $1 \leq i \leq k$ , and all the Lyapunov exponents are non-negative along $E^{c u}$ and non-positive along $E^{c s}$ , we prove the asymptotically random entropy expansiveness for $f$ .

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