Maximal tori in infinite-dimensional Hamiltonian systems: a Renormalization Group approach
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910409581133824 |
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| author | Corsi, Livia Gentile, Guido Procesi, Michela |
| author_facet | Corsi, Livia Gentile, Guido Procesi, Michela |
| contents | We study the existence of infinite-dimensional invariant tori in a mechanical system of infinitely many rotators weakly interacting with each other. We consider explicitly interactions depending only on the angles, with the aim of discussing in a simple case the analyticity properties to be required on the perturbation of the integrable system in order to ensure the persistence of a large measure set of invariant tori with finite energy. The proof we provide of the persistence of the invariant tori implements the Renormalization Group scheme based on the tree formalism -- i.e. the graphical representation of the solutions of the equations of motion in terms of trees -- which has been widely used in finite-dimensional problems. The method is very effectual and flexible: it naturally extends, once the functional setting has been fixed, to the infinite-dimensional case with only minor technical-natured adaptations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09025 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal tori in infinite-dimensional Hamiltonian systems: a Renormalization Group approach Corsi, Livia Gentile, Guido Procesi, Michela Dynamical Systems 37K55, 37K06 We study the existence of infinite-dimensional invariant tori in a mechanical system of infinitely many rotators weakly interacting with each other. We consider explicitly interactions depending only on the angles, with the aim of discussing in a simple case the analyticity properties to be required on the perturbation of the integrable system in order to ensure the persistence of a large measure set of invariant tori with finite energy. The proof we provide of the persistence of the invariant tori implements the Renormalization Group scheme based on the tree formalism -- i.e. the graphical representation of the solutions of the equations of motion in terms of trees -- which has been widely used in finite-dimensional problems. The method is very effectual and flexible: it naturally extends, once the functional setting has been fixed, to the infinite-dimensional case with only minor technical-natured adaptations. |
| title | Maximal tori in infinite-dimensional Hamiltonian systems: a Renormalization Group approach |
| topic | Dynamical Systems 37K55, 37K06 |
| url | https://arxiv.org/abs/2404.09025 |