Heterodimensional cycles, partial hyperbolicity and limit dynamics

• Type: Article in International Scientific Journal
• Date: 2002

Authors

Diaz, LJ (Author) Other; Rocha, J (Author) FCUP

Journal

Title: Fundamenta Mathematicae

Vol. 174

Pages: 127-186

ISSN: 0016-2736

Publisher: POLSKA AKADEMIA NAUK

Indexing

ISI Web of Knowledge - 27 Citations

Scopus - 27 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 60