Preprint D29/2006
Entropy-expansiveness and domination

Jose Vieitez | Pacifico, Maria Jose

**Keywords: **
Entropy-expansiveness | h-expansiveness | Dominated splitting

Let $f: M \to M$ be a $C^r$-diffeomorphism, $r\geq 1$, defined in
a compact boundary-less surface $M$. We prove that if $K$ is a
compact $f$-invariant subset of $M$ with a dominated splitting
then $f/K$ is $h$-expansive. Reciprocally, if there exists a $C^r$
neighborhood of $f$, ${\cal U}$, such that for $g\in {\cal U}$
there exists $K_g$ compact invariant such that $g/K_g$ is
$h$-expansive then there is a dominated splitting for $K_g$.