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Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics
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Pinto, A. A., Rand, D. A. (David A.) and Ferreira, E. (2007) Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics. Journal of Differential Equations, Vol.243 (No.2). pp. 168-178. doi:10.1016/j.jde.2007.02.013 ISSN 0022-0396.
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Official URL: http://dx.doi.org/10.1016/j.jde.2007.02.013
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Journal of Differential Equations | ||||
Publisher: | Academic Press | ||||
ISSN: | 0022-0396 | ||||
Official Date: | 15 December 2007 | ||||
Dates: |
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Volume: | Vol.243 | ||||
Number: | No.2 | ||||
Number of Pages: | 11 | ||||
Page Range: | pp. 168-178 | ||||
DOI: | 10.1016/j.jde.2007.02.013 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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