Periodic orbits and chain-transitive sets of C1-diffeomorphisms

• Autores: Sylvain Crovisier
• Localización: Publications Mathématiques de L'IHÉS, ISSN 0073-8301, Vol. 104, Nº. 1, 2006, págs. 87-141
• Idioma: inglés
• DOI: 10.1007/s10240-006-0002-4
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• Resumen

  • We prove that the chain-transitive sets of C1-generic diffeomorphisms are approximated in the Hausdorff topology by periodic orbits. This implies that the homoclinic classes are dense among the chain-recurrence classes.

    This result is a consequence of a global connecting lemma, which allows to build by a C1-perturbation an orbit connecting several prescribed points. One deduces a weak shadowing property satisfied by C1-generic diffeomorphisms: any pseudo-orbit is approximated in the Hausdorff topology by a finite segment of a genuine orbit. As a consequence, we obtain a criterion for proving the tolerance stability conjecture in Diff1(M).