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In this work we study the dynamical behavior Tonelli Lagrangian systemsdefined on the tangent bundle of the torus $\mathbb{T}^2=\mathbb{R}^2 /\mathbb{Z}^2$. We prove that the Lagrangian flow restricted to a high energylevel $ E_L^{-1}(c)$ (i.e $ c> c_0(L)$) has positive topological entropy if theflow satisfies the Kupka-Smale propriety in $ E_L^{-1}(c)$ (i.e, all closedorbit with energy $c$ are hyperbolic or elliptic and all heteroclinicintersections are transverse on $E_L^{-1}(c)$). The proof requires the use ofwell-known results in Aubry-Mather's Theory.

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