Heterodimensional cycles, partial hyperbolicity and limit dynamics

• Tipo: Artigo em Revista Científica Internacional
• Data: 2002

Autores

Diaz, LJ (Autor) Outra; Rocha, J (Autor) FCUP

Revista

Título: Fundamenta Mathematicae

Vol. 174

Páginas: 127-186

ISSN: 0016-2736

Editora: POLSKA AKADEMIA NAUK

Indexação

ISI Web of Knowledge - 27 Citações

Scopus - 27 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-000-R7C

DOI: 10.4064/fm174-2-2

Abstract (EN): We study one-parameter families of diffeomorphisms unfolding heterodimensional cycles (i.e. cycles containing periodic points of different indices). We construct an open set of such arcs such that, for a subset of the parameter space with positive relative density at the bifurcation value, the resulting nonwandering set is the disjoint union of two hyperbolic basic sets of different indices and a strong partially hyperbolic set which is robustly transitive. The dynamics of the diffeomorphisms we consider is partially hyperbolic with one-dimensional central direction. The main tool for proving our results is the construction of a one-dimensional model given by an iterated function system which describes the limit dynamics in the central direction. For selected parameters of the arc,. we translate properties of the model family to the diffeomorphisms.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 60