A note on Tonelli Lagrangian systems on T2 with positive topological entropy on a high energy level.
dc.contributor.author | Damasceno, Josué Geraldo | |
dc.contributor.author | Miranda, José Antônio Gonçalves | |
dc.contributor.author | Araújo, Luiz Gustavo Perona | |
dc.date.accessioned | 2023-02-06T20:44:36Z | |
dc.date.available | 2023-02-06T20:44:36Z | |
dc.date.issued | 2020 | pt_BR |
dc.description.abstract | In 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.citation | DAMASCENO, 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.doi | https://doi.org/10.20537/nd200407 | pt_BR |
dc.identifier.issn | 2658-5316 | |
dc.identifier.uri | http://www.repositorio.ufop.br/jspui/handle/123456789/16114 | |
dc.language.iso | en_US | pt_BR |
dc.rights | aberto | pt_BR |
dc.rights.license | This 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.subject | Aubry – mather theory | pt_BR |
dc.subject | Static classes | pt_BR |
dc.title | A note on Tonelli Lagrangian systems on T2 with positive topological entropy on a high energy level. | pt_BR |
dc.type | Artigo publicado em periodico | pt_BR |
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