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- W2004459616 abstract "We prove that given a compact n-dimensional boundaryless manifold M, n⩾2, there exists a residual subset R of Diff1(M) such that if f∈R admits a spectral decomposition (i.e., the non-wandering set Ω(f) admits a partition into a finite number of transitive compact sets), then this spectral decomposition is robust in a generic sense (tame behavior). This implies a C1-generic trichotomy that generalizes some aspects of a two-dimensional theorem of Mañé [Topology 17 (1978) 386–396]. Lastly, Palis [Astérisque 261 (2000) 335–347] has conjectured that densely in Diffk(M) diffeomorphisms either are hyperbolic or exhibit homoclinic bifurcations. We use the aforementioned results to prove this conjecture in a large open region of Diff1(M). Nous montrons qu'étant donnée une variété compacte M de dimension n, n⩾2, il existe un sous-ensemble résiduel R de Diff1(M) tel que si f∈R admet une décomposition spectrale (c'est-à-dire, Ω(f) admet une partition en un nombre fini d‘ensembles compacts transitifs), alors cette décomposition spectrale est robuste dans un sens générique. Cela implique une trichotomie générique qui généralise certains aspects d'un théorème bi-dimensionnel de Mañé. Enfin, Palis a conjecturé que dans un sous-ensemble dense de Diff1(M), les difféomorphismes ou bien sont hyperboliques, ou bien admettent des bifurcations homoclines. Nous utilisons les résultats précédents pour prouver cette conjecture dans une grande région ouverte de Diff1(M)." @default.
- W2004459616 created "2016-06-24" @default.
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- W2004459616 date "2003-03-01" @default.
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- W2004459616 title "Generic robustness of spectral decompositions" @default.
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- W2004459616 doi "https://doi.org/10.1016/s0012-9593(03)00008-9" @default.
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