On the Destruction of Invariant Lagrangian Graphs for Conformal Symplectic Twist Maps
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917985626619904 |
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| author | Sorrentino, Alfonso Wang, Lin |
| author_facet | Sorrentino, Alfonso Wang, Lin |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_06773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Destruction of Invariant Lagrangian Graphs for Conformal Symplectic Twist Maps Sorrentino, Alfonso Wang, Lin Dynamical Systems Symplectic Geometry 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. |
| title | On the Destruction of Invariant Lagrangian Graphs for Conformal Symplectic Twist Maps |
| topic | Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2504.06773 |