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Robustly expansive homoclinic classes

  • M. J. PACIFICO (a1), E. R. PUJALS (a1) and J. L. VIEITEZ (a2)

Let $f: M \to M$ be a diffeomorphism defined in a three-dimensional compact boundary-less manifold M. We prove that for an open dense set, C1-robustly expansive homoclinic classes H(p) for f are hyperbolic. A diffeomorphism f is $\alpha$-expansive on a compact invariant set K if there is $\alpha>0$ such that for all $x,y\in K$, if ${\rm dist}(f^n(x),f^n(y))\leq \alpha$ for all $n\in \mathbb Z$ then x = y. By ‘robustly’ we mean that there is $\alpha>0$ such that for all nearby diffeomorphisms g, the homoclinic class H(pg) of the continuation of p is $\alpha$-expansive.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
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