Hausdorff dimension versus smoothness
Data(s) |
02/12/2015
02/12/2015
2007
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Resumo |
There is a one-to-one correspondence between C1+H Cantor exchange systems that are C1+H fixed points of renormalization and C1+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 C1+α Cantor exchange system with bounded geometry that is a C1+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 C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. |
Identificador |
978-3-7643-8481-4 978-3-7643-8482-1 http://hdl.handle.net/10400.22/7045 10.1007/978-3-7643-8482-1_15 |
Idioma(s) |
eng |
Publicador |
Birkhäuser Basel |
Relação |
http://link.springer.com/chapter/10.1007%2F978-3-7643-8482-1_15 |
Direitos |
closedAccess |
Palavras-Chave | #Hyperbolic systems #Attractors #Hausdorff dimension |
Tipo |
bookPart |