Improved stability estimates at elliptic equilibria of Hamiltonian systems
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918305376239616 |
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| author | Guzzo, Massimiliano Caracciolo, Chiara Pinzari, Gabriella |
| author_facet | Guzzo, Massimiliano Caracciolo, Chiara Pinzari, Gabriella |
| contents | This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian system satisfying a non-resonance condition of finite order N. In particular, we improve the standard a-priori lower bound on the stability time from a purely linear dependence on the inverse of the polynomial norm of the remainder of the normal form to the sum of a linear term (which is still present but with a different constant coefficient) and a quadratic one. The prevalence between the linear and the quadratic term depends on the resonance properties of all the monomials in the remainder of the normal form with degree from N to a finite order M. We also provide a comparative example of the new estimates and the traditional a priori ones in the framework of computer-assisted proofs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18268 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Improved stability estimates at elliptic equilibria of Hamiltonian systems Guzzo, Massimiliano Caracciolo, Chiara Pinzari, Gabriella Dynamical Systems Mathematical Physics This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian system satisfying a non-resonance condition of finite order N. In particular, we improve the standard a-priori lower bound on the stability time from a purely linear dependence on the inverse of the polynomial norm of the remainder of the normal form to the sum of a linear term (which is still present but with a different constant coefficient) and a quadratic one. The prevalence between the linear and the quadratic term depends on the resonance properties of all the monomials in the remainder of the normal form with degree from N to a finite order M. We also provide a comparative example of the new estimates and the traditional a priori ones in the framework of computer-assisted proofs. |
| title | Improved stability estimates at elliptic equilibria of Hamiltonian systems |
| topic | Dynamical Systems Mathematical Physics |
| url | https://arxiv.org/abs/2601.18268 |