Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics

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

Autores

Pinto, AA (Autor) FCUP; Rand, DA (Autor) Outra; Ferreira, E (Autor) Outra

Revista

Título: Journal of Differential Equations

Vol. 243

Páginas: 168-178

ISSN: 0022-0396

Editora: Elsevier

Indexação

ISI Web of Knowledge - 6 Citações

Scopus - 6 Citações

Classificação Científica

FOS: Ciências exactas e naturais > Matemática

Outras Informações

ID Authenticus: P-004-5RK

DOI: 10.1016/j.jde.2007.02.013

Resumo (PT): We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a C^r diffeomorphism f of a surface, are not C^{1+θ} for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.

Abstract (EN): We prove that the stable holonomies of a proper codimension 1 attractor Lambda, for a C-r diffeomorphism f of a surface, are not C1+theta for theta greater than the Hausdorff dimension of the stable leaves of f intersected with Lambda. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.

Idioma: Inglês

Tipo (Avaliação Docente): Científica

Nº de páginas: 11