Abstract (EN):
In this paper we study C-1-structurally stable diffeomorphisms, that is, C-1 Axiom A diffeomorphisms with the strong transversality condition. In contrast to the case of dynamics restricted to a hyperbolic basic piece, structurally stable diffeomorphisms are in general not expansive and the conjugacies between C-1-close structurally stable diffeomorphisms may be non-unique, even if there are assumed C-0-close to the identity. Here we give a necessary and sufficient condition for a structurally stable diffeomorphism to admit a dense subset of points with expansiveness and sensitivity to initial conditions. Morever, we prove that the set of conjugacies between elements in the same conjugacy class is homeomorphic to the C-0-centralizer of the dynamics. Finally, we use this fact to deduce that any two C-1-close structurally stable diffeomorphisms are conjugated by a unique conjugacy C-0-close to the identity if and only if these are Anosov.
Idioma:
Inglês
Tipo (Avaliação Docente):
Científica
Nº de páginas:
21