Quantitative contact Hamiltonian dynamics
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918128814915584 |
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| author | Djordjević, Danijel Uljarević, Igor Zhang, Jun |
| author_facet | Djordjević, Danijel Uljarević, Igor Zhang, Jun |
| contents | This paper presents a systematic quantitative study of contact rigidity phenomena based on the contact Hamiltonian Floer theory established by Merry-Uljarević. Our quantitative approach applies to arbitrary admissible contact Hamiltonian functions on the contact boundary $M = \partial W$ of a ${\rm weakly}^{+}$-monotone symplectic manifold $W$. From a theoretical standpoint, we develop a comprehensive contact spectral invariant theory. As applications, the properties of these invariants enable us to establish several fundamental results: the contact big fiber theorem, sufficient conditions for orderability, and the existence results of translated points. Furthermore, we uncover a non-traditional filtration structure on contact Hamiltonian Floer groups, which we formalize through the introduction of a novel type of persistence modules, called gapped modules, that are only parametrized by a partially ordered set. Among the various properties of contact spectral invariants, we highlight that the triangle inequality is derived through an innovative analysis of a pair-of-pants construction in the contact-geometric framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13234 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantitative contact Hamiltonian dynamics Djordjević, Danijel Uljarević, Igor Zhang, Jun Symplectic Geometry Dynamical Systems 53D40, 55U99, 53D35 This paper presents a systematic quantitative study of contact rigidity phenomena based on the contact Hamiltonian Floer theory established by Merry-Uljarević. Our quantitative approach applies to arbitrary admissible contact Hamiltonian functions on the contact boundary $M = \partial W$ of a ${\rm weakly}^{+}$-monotone symplectic manifold $W$. From a theoretical standpoint, we develop a comprehensive contact spectral invariant theory. As applications, the properties of these invariants enable us to establish several fundamental results: the contact big fiber theorem, sufficient conditions for orderability, and the existence results of translated points. Furthermore, we uncover a non-traditional filtration structure on contact Hamiltonian Floer groups, which we formalize through the introduction of a novel type of persistence modules, called gapped modules, that are only parametrized by a partially ordered set. Among the various properties of contact spectral invariants, we highlight that the triangle inequality is derived through an innovative analysis of a pair-of-pants construction in the contact-geometric framework. |
| title | Quantitative contact Hamiltonian dynamics |
| topic | Symplectic Geometry Dynamical Systems 53D40, 55U99, 53D35 |
| url | https://arxiv.org/abs/2507.13234 |