Abstract
We show that diffeomorphisms with a dominated splitting ofthe form $E^s\oplus E^c\oplus E^u$, where $E^c$ is a nonhyperboliccentral bundle that splits in a dominated way into1-dimensional subbundles, are entropy-expansive.In particular, they have a principal symbolic extension and equilibrium states.
Highlights
In dynamical systems one often considers the following three main levels of structure: measure theoretic, topological, and infinitesimal
We will focus on a special type of partial hyperbolicity that will ensure the system is entropyexpansive
In [PV1] for a surface diffeomorphisms f and a compact f invariant set Λ with a dominated splitting it is shown that the map f restricted to Λ is entropy-expansive
Summary
In dynamical systems one often considers the following three main levels of structure: measure theoretic, topological, and infinitesimal (properties of the derivative). Entropy-expansive, equilibrium state, partially hyperbolic, dominated splitting, symbolic extension.
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