Publication
Dense area-preserving homeomorphisms have zero Lyapunov exponents
| dc.contributor.author | Bessa, Mário | |
| dc.contributor.author | M. Silva, César | |
| dc.date.accessioned | 2023-05-25T08:54:09Z | |
| dc.date.available | 2023-05-25T08:54:09Z | |
| dc.date.issued | 2012 | |
| dc.description.abstract | We give a new definition (different from the one in [14]) for a Lyapunov exponent (called new Lyapunov exponent) associated to a continuous map. Our first result states that these new exponents coincide with the usual Lyapunov exponents if the map is differentiable. Then, we apply this concept to prove that there exists a C0-dense subset of the set of the area-preserving homeomorphisms defined in a compact, connected and boundaryless surface such that any element inside this residual subset has zero new Lyapunov exponents for Lebesgue almost every point. Finally, we prove that the function that associates an area-preserving homeomorphism, equipped with the C0-topology, to the integral (with respect to area) of its top new Lyapunov exponent over the whole surface cannot be upper-semicontinuous. | pt_PT |
| dc.description.sponsorship | MB was partially supported by FCT - Fundação para a Ciência e a Tecnologia through CMUP (SFRH/BPD/20890/2004) and CS was partially supported by FCT through CMUBI (FCT/POCI2010/FEDER). CS would like to thank Luís Barreira for fruitful conversations aiming the definition of the exponents for continuous transformations. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | M. Bessa, C. M. Silva, Dense area-preserving homeomorphisms have zero Lyapunov exponents, Discrete & Continuous Dynamical Systems - A, 32, 4, 1231-1244, 2012 | pt_PT |
| dc.identifier.doi | 10.3934/dcds.2012.32.1231 | pt_PT |
| dc.identifier.issn | 1078-0947 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/13832 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | AIMS | pt_PT |
| dc.relation | ABUNDÂNCIA DE EXPOENTES DE IYAPUNOV ZERO EM SISTEMAS CONSERVATIVOS A TEMPO CONTÍNUO | |
| dc.relation.publisherversion | https://www.aimsciences.org/article/doi/10.3934/dcds.2012.32.1231 | pt_PT |
| dc.subject | Area-preserving homeomorphisms | pt_PT |
| dc.subject | Lyapunov exponents | pt_PT |
| dc.subject | Topological dynamics | pt_PT |
| dc.title | Dense area-preserving homeomorphisms have zero Lyapunov exponents | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | ABUNDÂNCIA DE EXPOENTES DE IYAPUNOV ZERO EM SISTEMAS CONSERVATIVOS A TEMPO CONTÍNUO | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/FARH/SFRH%2FBPD%2F20890%2F2004/PT | |
| oaire.citation.endPage | 1244 | pt_PT |
| oaire.citation.issue | 4 | pt_PT |
| oaire.citation.startPage | 1231 | pt_PT |
| oaire.citation.title | Discrete & Continuous Dynamical Systems - Series A | pt_PT |
| oaire.citation.volume | 32 | pt_PT |
| oaire.fundingStream | FARH | |
| person.familyName | Bessa | |
| person.givenName | Mário | |
| person.identifier | https://scholar.google.com/citations?user=088yCR4AAAAJ&hl=pt-PT | |
| person.identifier.ciencia-id | C21A-EEC0-A3EF | |
| person.identifier.orcid | 0000-0002-1758-2225 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | restrictedAccess | pt_PT |
| rcaap.type | article | pt_PT |
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