Publication
Anosov diffeomorphisms, renormalization and tilings
| dc.contributor.advisor | Pinto, Alberto A. | |
| dc.contributor.author | Almeida, João P. | |
| dc.date.accessioned | 2014-11-06T09:14:13Z | |
| dc.date.available | 2014-11-06T09:14:13Z | |
| dc.date.issued | 2012 | |
| dc.description.abstract | In this thesis, we prove a one-to-one correspondence between C^{1+} smooth conjugacy classes of circle diffeomorphisms that are C^{1+} fixed points of renormalization and C^{1+} conjugacy classes of Anosov diffeomorphisms whose Sinai-Ruelle-Bowen measure is absolutely continuous with respect to Lebesgue measure. Furthermore, we use ratio functions to parametrize the infinite dimensional space of C^{1+} smooth conjugacy classes of circle diffeomorphisms that are C^{1+} fixed points of renormalization. We introduce the notion of γ-tilings and we prove a one-to-one correspondence between (i) smooth conjugacy classes of Anosov diffeomorphisms, with an invariant measure absolutely continuous with respect to the Lebesgue measure, (ii) affine classes of γ-tilings and (iii) solenoid functions. The solenoid functions give a parametrization of the infinite dimensional space consisting of the mathematical objects described in the above equivalences. | por |
| dc.identifier.tid | 101350066 | |
| dc.identifier.uri | http://hdl.handle.net/10198/11344 | |
| dc.language.iso | eng | por |
| dc.subject | Mathematics | |
| dc.subject | Dynamical systems | |
| dc.title | Anosov diffeomorphisms, renormalization and tilings | por |
| dc.type | doctoral thesis | |
| dspace.entity.type | Publication | |
| person.familyName | Almeida | |
| person.givenName | João P. | |
| person.identifier | R-000-K6T | |
| person.identifier.ciencia-id | 1C14-D6B1-6A78 | |
| person.identifier.orcid | 0000-0002-1286-2527 | |
| person.identifier.rid | N-8243-2013 | |
| person.identifier.scopus-author-id | 54956738400 | |
| rcaap.rights | openAccess | por |
| rcaap.type | doctoralThesis | por |
| relation.isAuthorOfPublication | d51506e1-376c-4c70-b68b-f527b54440d2 | |
| relation.isAuthorOfPublication.latestForDiscovery | d51506e1-376c-4c70-b68b-f527b54440d2 | |
| thesis.degree.discipline | Matemática | por |
| thesis.degree.level | Doutoramento em Matemática Aplicada | por |