A note on Tonelli Lagrangian systems on T2 with positive topological entropy on a high energy level.

dc.contributor.authorDamasceno, Josué Geraldo
dc.contributor.authorMiranda, José Antônio Gonçalves
dc.contributor.authorAraújo, Luiz Gustavo Perona
dc.date.accessioned2023-02-06T20:44:36Z
dc.date.available2023-02-06T20:44:36Z
dc.date.issued2020pt_BR
dc.description.abstractIn this work we study the dynamical behavior of Tonelli Lagrangian systems defined on the tangent bundle of the torus T2 = R2/Z2. We prove that the Lagrangian flow restricted to a high energy level E−1 L (c) (i.e., c>c0(L)) has positive topological entropy if the flow satisfies the Kupka-Smale property in E−1 L (c) (i.e., all closed orbits with energy c are hyperbolic or elliptic and all heteroclinic intersections are transverse on E−1 L (c)). The proof requires the use of well-known results from Aubry – Mather theory.pt_BR
dc.identifier.citationDAMASCENO, J. G.; MIRANDA, J. A. G.; ARAÚJO, L. G. P. A note on Tonelli Lagrangian systems on T2 with positive topological entropy on a high energy level. Nelineinaya Dinamika, v. 16, n. 4, p. 625-635, 2020. Disponível em: <http://nd.ics.org.ru/nd200407/>. Acesso em: 06 jul. 2022.pt_BR
dc.identifier.doihttps://doi.org/10.20537/nd200407pt_BR
dc.identifier.issn2658-5316
dc.identifier.urihttp://www.repositorio.ufop.br/jspui/handle/123456789/16114
dc.language.isoen_USpt_BR
dc.rightsabertopt_BR
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License. Fonte: Russian Journal of Nonlinear Dynamics <http://nd.ics.org.ru/nd200407/>. Acesso em: 19 out. 2022.pt_BR
dc.subjectAubry – mather theorypt_BR
dc.subjectStatic classespt_BR
dc.titleA note on Tonelli Lagrangian systems on T2 with positive topological entropy on a high energy level.pt_BR
dc.typeArtigo publicado em periodicopt_BR

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