On the volume of singular-hyperbolic sets

• Tipo: Artigo em Revista Científica Internacional
• Data: 2007

Autores

alves, jf (Autor) FCUP; arauo, v (Autor) Outra; pacifico, mj (Autor) Outra; pinheiro, v (Autor) Outra

Revista

Título: Dynamical Systems

Vol. 22

Páginas: 249-267

ISSN: 1468-9367

Editora: Taylor & Francis

Indexação

ISI Web of Knowledge - 10 Citações

Scopus - 12 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-004-CYY

DOI: 10.1080/14689360601165217

Abstract (EN): An attractor Lambda for a 3-vector field X is singular-hyperbolic if all its singularities are hyperbolic and it is partially hyperbolic with volume expanding central direction. We prove that C1+alpha singular-hyperbolic attractors, for any alpha > 0, always have zero volume, extending an analogous result for uniformly hyperbolic attractors. The same result holds for a class of higher dimensional singular attractors. Moreover, we prove that if Lambda is a singular-hyperbolic attractor for X then either it has zero volume or X is an Anosov flow. We also present examples of C-1 singular-hyperbolic attractors with positive volume. In addition, we show that C-1 generically we have volume zero for C-1 robust classes of singular-hyperbolic attractors.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 19