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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2002 | 174 | 2 | 127-186

## Heterodimensional cycles, partial hyperbolicity and limit dynamics

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.

127-186

wydano
2002

### Twórcy

autor
• Depto. Matemática PUC-Rio, Marquês de S. Vicente núm. 225, 22453-900 Rio de Janeiro RJ, Brazil
autor
• Departamento de Matemática Pura, Universidade do Porto, Rua do Campo Alegre núm. 687, 4169-007 Porto, Portugal