Please use this identifier to cite or link to this item: http://www.repositorio.ufop.br/jspui/handle/123456789/16114
Title: A note on Tonelli Lagrangian systems on T2 with positive topological entropy on a high energy level.
Authors: Damasceno, Josué Geraldo
Miranda, José Antônio Gonçalves
Araújo, Luiz Gustavo Perona
Keywords: Aubry – mather theory
Static classes
Issue Date: 2020
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.
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.
URI: http://www.repositorio.ufop.br/jspui/handle/123456789/16114
metadata.dc.identifier.doi: https://doi.org/10.20537/nd200407
ISSN: 2658-5316
metadata.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.
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