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Języki publikacji
Abstrakty
We discuss the remaining obstacles to prove Smale's conjecture about the C¹-density of hyperbolicity among surface diffeomorphisms. Using a C¹-generic approach, we classify the possible pathologies that may obstruct the C¹-density of hyperbolicity. We show that there are essentially two types of obstruction: (i) persistence of infinitely many hyperbolic homoclinic classes and (ii) existence of a single homoclinic class which robustly exhibits homoclinic tangencies. In the course of our discussion, we obtain some related results about C¹-generic properties of surface diffeomorphisms involving homoclinic classes, chain-recurrence classes, and hyperbolicity. In particular, it is shown that on a connected surface the C¹-generic diffeomorphisms whose non-wandering sets have non-empty interior are the Anosov diffeomorphisms.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
127-159
Opis fizyczny
Daty
wydano
2005
Twórcy
autor
- IMPA, Estrada dona Castorina 110, CEP 222460-320, Rio de Janeiro, RJ, Brazil
autor
- CNRS - IMB, UMR 5584, BP 47 870, 21078 Dijon Cedex, France
autor
- CNRS - LAGA, UMR 7539, Université Paris 13, Av. J.-B. Clément, 93430 Villetaneuse, France
autor
- Dep. Matemática PUC-Rio, Marquês de S. Vicente 225, CEP 22453-900, Rio de Janeiro, RJ, Brazil
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-fm187-2-3