A note on Tonelli Lagrangian systems on ${\mathbb{T}}^2$ with positive topological entropy on high energy level

J. G. Damasceno, J. A. G. Miranda, L. G. Perona

In this work we study the dynamical behavior Tonelli Lagrangian systems defined on the tangent bundle of the torus ${\mathbb{T}}^2={\mathbb{R}}^2/{\mathbb{Z}}^2$. We prove that the Lag…