Ergodic closing lemmas and invariant Lagrangians
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912243676872704 |
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| author | Cineli, Erman Seyfaddini, Sobhan Tanny, Shira |
| author_facet | Cineli, Erman Seyfaddini, Sobhan Tanny, Shira |
| contents | Motivated by the ergodic closing lemma of Mañé, we investigate the $C^\infty$ closing lemma in higher-dimensional Hamiltonian systems, with a focus on the statistical behavior of periodic orbits generated by $C^\infty$-small perturbations. We demonstrate that, under certain Floer-theoretic conditions, invariant or recurrent Lagrangian submanifolds can give rise to periodic orbits whose statistical properties are controllable. For instance, we show that for Hamiltonian systems preserving the zero section in $T^*\mathbb{T}^n$, $C^\infty$ generically, there exist periodic orbits converging to an invariant measure supported on the zero section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11566 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodic closing lemmas and invariant Lagrangians Cineli, Erman Seyfaddini, Sobhan Tanny, Shira Dynamical Systems Symplectic Geometry Motivated by the ergodic closing lemma of Mañé, we investigate the $C^\infty$ closing lemma in higher-dimensional Hamiltonian systems, with a focus on the statistical behavior of periodic orbits generated by $C^\infty$-small perturbations. We demonstrate that, under certain Floer-theoretic conditions, invariant or recurrent Lagrangian submanifolds can give rise to periodic orbits whose statistical properties are controllable. For instance, we show that for Hamiltonian systems preserving the zero section in $T^*\mathbb{T}^n$, $C^\infty$ generically, there exist periodic orbits converging to an invariant measure supported on the zero section. |
| title | Ergodic closing lemmas and invariant Lagrangians |
| topic | Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2502.11566 |