DCDS
Entropy-expansiveness for partially hyperbolic diffeomorphisms
Lorenzo J. Díaz Todd Fisher M. J. Pacifico José L. Vieitez
Discrete & Continuous Dynamical Systems - A 2012, 32(12): 4195-4207 doi: 10.3934/dcds.2012.32.4195
We show that diffeomorphisms with a dominated splitting of the form $E^s\oplus E^c\oplus E^u$, where $E^c$ is a nonhyperbolic central bundle that splits in a dominated way into 1-dimensional subbundles, are entropy-expansive. In particular, they have a principal symbolic extension and equilibrium states.
keywords: symbolic extension. Entropy-expansive dominated splitting equilibrium state partially hyperbolic
DCDS
On $C^1$-persistently expansive homoclinic classes
Martín Sambarino José L. Vieitez
Discrete & Continuous Dynamical Systems - A 2006, 14(3): 465-481 doi: 10.3934/dcds.2006.14.465
Let $f: M \to M$ be a diffeomorphism defined in a $d$-dimensional compact boundary-less manifold $M$. We prove that $C^1$-persistently expansive homoclinic classes $H(p)$, $p$ an $f$-hyperbolic periodic point, have a dominated splitting $E\oplus F$, $\dim(E)=\mbox{index}(p)$. Moreover, we prove that if the $H(p)$-germ of $f$ is expansive (in particular if $H(p)$ is an attractor, repeller or maximal invariant) then it is hyperbolic.
keywords: hyperbolicity Expansiveness homoclinic classes. dominated splitting
DCDS
Robustly expansive homoclinic classes are generically hyperbolic
Martín Sambarino José L. Vieitez
Discrete & Continuous Dynamical Systems - A 2009, 24(4): 1325-1333 doi: 10.3934/dcds.2009.24.1325
Let $f: M \to M$ be a diffeomorphism defined in a $d$-dimensional compact boundary-less manifold $M$. We prove that generically $C^1$-robustly expansive homoclinic classes $H(p)$, $p$ an $f$-hyperbolic periodic point, are hyperbolic.
keywords: Dominated Splitting Hyperbolicity Expansiveness Homoclinic Classes.

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