Hausdorff dimension versus smoothness

• Type: Chapter or Part of a Book
• Date: 2008

Authors

Ferreira, F (Author) Other; Alberto A. Pinto (Author) Other; Rand, DA (Author) Other

Indexing

Scopus - 1 Citation

Other information

Authenticus ID: P-00H-1MJ

DOI: 10.1007/978-3-7643-8482-1_15

Abstract (EN): 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 ¿ that admit an invariant measure absolutely continuous with respect to the Hausdorff measure on ¿. However, there is no such C 1+¿ Cantor exchange system with bounded geometry that is a C 1+¿ fixed point of renormalization with regularity ¿ 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 ¿ are not C 1+¿ for ¿ greater than the Hausdorff dimension of the stable leaves of f intersected with ¿. © 2007, Birkhäuser Verlag Basel/Switzerland.

Language: English

Type (Professor's evaluation): Scientific