Heterodimensional cycles, partial hyperbolicity and limit dynamics

• Autorzy: L. J. Diaz , J. Rocha
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 37D30: Partially hyperbolic systems and dominated splittings
• 37C20: Generic properties, structural stability

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2002
• Tom: 174
• Numer: 2
• Strony: 127-186

Daty

wydano

2002

Twórcy

autor

L. J. Diaz

• Depto. Matemática PUC-Rio, Marquês de S. Vicente núm. 225, 22453-900 Rio de Janeiro RJ, Brazil

autor

J. Rocha

• Departamento de Matemática Pura, Universidade do Porto, Rua do Campo Alegre núm. 687, 4169-007 Porto, Portugal

Identyfikatory

DOI

10.4064/fm174-2-2