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Hausdorff dimension versus smoothness
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Ferreira, Flávio, Pinto, Alberto A. and Rand, D. A. (David A.) (2008) Hausdorff dimension versus smoothness. In: Staicu, Vasile, (ed.) Differential Equations, Chaos and Variational Problems. Progress in nonlinear differential equations and their applications, Volume 75 . Basel: Birkhäuser, pp. 195-209. ISBN 9783764384814
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Official URL: http://dx.doi.org/10.1007/978-3-7643-8482-1_15
Abstract
There is a one-to-one correspondence between C 1+H Cantor exchange systems that are C 1+H fixed points of renormalization and C 1+H diffeomorphisms f on surfaces with a codimension 1 hyperbolic attractor Λ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on Λ. However, there is no such C 1+α Cantor exchange system with bounded geometry that is a C 1+α fixed point of renormalization with regularity α greater than the Hausdorff dimension of its invariant Cantor set. The proof of the last result uses that the stable holonomies of a codimension 1 hyperbolic attractor Λ are not C 1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ.
Item Type: | Book Item | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Series Name: | Progress in nonlinear differential equations and their applications | ||||
Publisher: | Birkhäuser | ||||
Place of Publication: | Basel | ||||
ISBN: | 9783764384814 | ||||
Book Title: | Differential Equations, Chaos and Variational Problems | ||||
Editor: | Staicu, Vasile | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Volume 75 | ||||
Number of Pages: | 435 | ||||
Page Range: | pp. 195-209 | ||||
DOI: | 10.1007/978-3-7643-8482-1_15 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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