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https://hdl.handle.net/10216/101972| Author(s): | Pinto, AA Rand, DA Ferreira, E |
| Title: | Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics |
| Issue Date: | 2007 |
| 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. |
| 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. |
| Subject: | Matemática Mathematics |
| Scientific areas: | Ciências exactas e naturais::Matemática Natural sciences::Mathematics |
| URI: | https://hdl.handle.net/10216/101972 |
| Document Type: | Artigo em Revista Científica Internacional |
| Rights: | restrictedAccess |
| Appears in Collections: | FCUP - Artigo em Revista Científica Internacional |
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|---|---|---|---|---|
| 48114.pdf Restricted Access | 181.95 kB | Adobe PDF | Request a copy from the Author(s) |
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