On sensitivity to initial conditions and uniqueness of conjugacies for structurally stable diffeomorphisms

• Type: Article in International Scientific Journal
• Date: 2018

Authors

Jorge Rocha (Author) FCUP; Varandas, P (Author) FCUP

Journal

Title: Nonlinearity

Vol. 31

Pages: 293-313

ISSN: 0951-7715

Publisher: Institute of Physics Publishing

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 1 Citation

Other information

Authenticus ID: P-00N-B7T

DOI: 10.1088/1361-6544/aa8d78

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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 21