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

Pinto, AA; Rand, DA; Ferreira, E

doi:10.1016/j.jde.2007.02.013

Please use this identifier to cite or link to this item: https://hdl.handle.net/10216/101972

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DC Field	Value	Language
dc.creator	Pinto, AA
dc.creator	Rand, DA
dc.creator	Ferreira, E
dc.date.accessioned	2022-09-10T17:59:01Z	-
dc.date.available	2022-09-10T17:59:01Z	-
dc.date.issued	2007
dc.identifier.issn	0022-0396
dc.identifier.other	sigarra:48114
dc.identifier.uri	https://hdl.handle.net/10216/101972	-
dc.description	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.
dc.description.abstract	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.
dc.language.iso	eng
dc.rights	restrictedAccess
dc.subject	Matemática
dc.subject	Mathematics
dc.title	Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
dc.type	Artigo em Revista Científica Internacional
dc.contributor.uporto	Faculdade de Ciências
dc.identifier.doi	10.1016/j.jde.2007.02.013
dc.identifier.authenticus	P-004-5RK
dc.subject.fos	Ciências exactas e naturais::Matemática
dc.subject.fos	Natural sciences::Mathematics
Appears in Collections:	FCUP - Artigo em Revista Científica Internacional

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