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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2312.01695 |
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| _version_ | 1866909355169808384 |
|---|---|
| author | Wang, Lin |
| author_facet | Wang, Lin |
| contents | For an integrable Hamiltonian systems with $d$ degrees of freedom ($d\geq 2$), we consider quantitatively the existence and non-existence of the flow-invariant Lagrangian torus with given frequency under the perturbation beyond the scope of the classical KAM method in the $C^r$ topology. As applications, the non-existence result gives a partial answer to an open problem on non-existence of invariant circles by Mather from 1988. The existence result sheds a light on another open problem on the existence of invariant circles with lower regularity by Mather from 1998. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01695 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantitative Destruction and Persistence of Lagrangian Torus in Hamiltonian Systems Wang, Lin Dynamical Systems For an integrable Hamiltonian systems with $d$ degrees of freedom ($d\geq 2$), we consider quantitatively the existence and non-existence of the flow-invariant Lagrangian torus with given frequency under the perturbation beyond the scope of the classical KAM method in the $C^r$ topology. As applications, the non-existence result gives a partial answer to an open problem on non-existence of invariant circles by Mather from 1988. The existence result sheds a light on another open problem on the existence of invariant circles with lower regularity by Mather from 1998. |
| title | Quantitative Destruction and Persistence of Lagrangian Torus in Hamiltonian Systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2312.01695 |