ESEIG - MAT - Livros, partes de livro ou capítulos de livro
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Browsing ESEIG - MAT - Livros, partes de livro ou capítulos de livro by Author "Rand, David A."
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- Fine structures of hyperbolic diffeomorphismsPublication . Pinto, Alberto A.; Rand, David A.; Ferreira, Flávio
- Hausdorff dimension versus smoothnessPublication . Ferreira, Flávio; Pinto, Alberto A.; Rand, David A.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.