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

• Autor(a) principal: Damasceno, Josué Geraldo
• Data de Publicação: 2020
• Outros Autores: Miranda, José Antônio Gonçalves, Araújo, Luiz Gustavo Perona
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UFOP
• Texto Completo: http://www.repositorio.ufop.br/jspui/handle/123456789/16114; https://doi.org/10.20537/nd200407
• topic: Aubry – mather theory; Static classes

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.