论文标题
$ \ mathbb {t}^2 $上的Tonelli Lagrangian Systems的注释，高能量上有正拓扑熵
A note on Tonelli Lagrangian systems on $\mathbb{T}^2$ with positive topological entropy on high energy level
论文作者
论文摘要
在这项工作中，我们研究了动态行为Tonelli Lagrangian系统在圆环$ \ mathbb {t}^2 = \ mathbb {r}^2 / \ mathbb {z}^2 $上定义的。我们证明，如果流动满足kupka-smale的适当性，则限制在高能水平$ e_l^{ - 1}（c）$（即$ c> c_0（l）$）具有积极的拓扑熵。 $ e_l^{ - 1}（c）$）的横向。证明需要在奥布里·梅瑟（Aubry-Mather）理论中使用众所周知的结果。
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 Lagrangian flow restricted to a high energy level $ E_L^{-1}(c)$ (i.e $ c> c_0(L)$) has positive topological entropy if the flow satisfies the Kupka-Smale propriety in $ E_L^{-1}(c)$ (i.e, all closed orbit with energy $c$ are hyperbolic or elliptic and all heteroclinic intersections are transverse on $E_L^{-1}(c)$). The proof requires the use of well-known results in Aubry-Mather's Theory.
