| dc.contributor.author | Ferreira, Flávio | |
| dc.contributor.author | Pinto, Alberto A. | |
| dc.contributor.author | Rand, David A. | |
| dc.date.accessioned | 2015-12-02T10:56:11Z | |
| dc.date.available | 2015-12-02T10:56:11Z | |
| dc.date.issued | 2007 | |
| dc.description.abstract | 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. | pt_PT |
| dc.description.sponsorship | We are very grateful to Welington de Melo and Stefano Luzzatto for very useful discussions on this work. We thank IHES, CUNY, IMPA, Stony Brook and University of Warwick for their hospitality. We thank Calouste Gulbenkian Foundation, PRODYN-ESF, POCTI and POCI by FCT and Ministério da Ciência, Tecnologia e do Ensino Superior, and Centro de Matemática da Universidade do Porto for their financial support of A. A. Pinto and F. Ferreira. | |
| dc.identifier.doi | 10.1007/978-3-7643-8482-1_15 | pt_PT |
| dc.identifier.isbn | 978-3-7643-8481-4 | |
| dc.identifier.isbn | 978-3-7643-8482-1 | |
| dc.identifier.uri | http://hdl.handle.net/10400.22/7045 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Birkhäuser Basel | pt_PT |
| dc.relation.publisherversion | http://link.springer.com/chapter/10.1007%2F978-3-7643-8482-1_15 | pt_PT |
| dc.subject | Hyperbolic systems | pt_PT |
| dc.subject | Attractors | pt_PT |
| dc.subject | Hausdorff dimension | pt_PT |
| dc.title | Hausdorff dimension versus smoothness | pt_PT |
| dc.type | book part | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 209 | pt_PT |
| oaire.citation.startPage | 195 | pt_PT |
| oaire.citation.title | Differential Equations, Chaos and Variational Problems | pt_PT |
| person.familyName | Ferreira | |
| person.givenName | Flávio | |
| person.identifier.ciencia-id | 9F13-D3C6-244B | |
| person.identifier.orcid | 0000-0001-7812-0983 | |
| person.identifier.rid | N-4562-2013 | |
| person.identifier.scopus-author-id | 22978799800 | |
| rcaap.rights | closedAccess | pt_PT |
| rcaap.type | bookPart | pt_PT |
| relation.isAuthorOfPublication | 6f67981a-3965-4ace-aec9-65938c4bcf66 | |
| relation.isAuthorOfPublication.latestForDiscovery | 6f67981a-3965-4ace-aec9-65938c4bcf66 |
