标题： 关于保形辛扭转映射中不变拉格朗日图的破坏 显示英文标题

标题： On the Destruction of Invariant Lagrangian Graphs for Conformal Symplectic Twist Maps

摘要： 本文研究耗散映射中不变拉格朗日图的脆弱性，重点关注在小扰动下的破坏情况。受赫尔曼关于保守系统的成果启发，我们证明了可积耗散扭转映射的所有$C^0$- 不变拉格朗日图都可以通过在$C^{1-\varepsilon}$- 拓扑意义下任意小的扰动来破坏。这一结果是最优的，由正常双曲不变流形定理保证的$C^1$- 不变量图在$C^1$- 扰动下的持续性即可体现。 显示英文摘要

摘要： In this article we investigate the fragility of invariant Lagrangian graphs for dissipative maps, focusing on their destruction under small perturbations. Inspired by Herman's work on conservative systems, we prove that all $C^0$-invariant Lagrangian graphs for an integrable dissipative twist maps can be destroyed by perturbations that are arbitrarily small in the $C^{1-\varepsilon}$-topology. This result is sharp, as evidenced by the persistence of $C^1$-invariant graphs under $C^1$-perturbations guaranteed by the normally hyperbolic invariant manifold theorem.