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

• Type: Article in International Scientific Journal
• Date: 2007

Authors

Pinto, AA (Author) FCUP; Rand, DA (Author) Other; Ferreira, E (Author) Other

Journal

Title: Journal of Differential Equations

Vol. 243

Pages: 168-178

ISSN: 0022-0396

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 6 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 11