On maximal transitive sets of generic diffeomorphisms
Christian Bonatti, Lorenzo J. Díaz (2003)
Publications Mathématiques de l'IHÉS
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Displaying similar documents to “Generic robustness of spectral decompositions”
On maximal transitive sets of generic diffeomorphisms
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We prove that the chain-transitive sets of C-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 C-perturbation an orbit connecting several prescribed points. One deduces a weak shadowing property satisfied by C-generic diffeomorphisms: any pseudo-orbit is approximated in the Hausdorff...