Integrable perturbations of polynomial Hamiltonian systems
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914540078235648 |
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| author | Treschev, Dmitry |
| author_facet | Treschev, Dmitry |
| contents | We consider a Hamiltonian system on the symplectic space $({\mathbb{R}}^{2n}, dy\wedge dx)$ with a real-analytic Hamiltonian $H : {\mathbb{R}}^{2n}\to {\mathbb{R}}$. We assume that the system has a non-degenerate equilibrium position at the origin. Under some nonresonance assumptions we prove the following.
For any positive integer $M$ there exists a real-analytic function $F:{\mathbb{R}}^{2n}\to{\mathbb{R}}$ such that
(1) $F = O\big( (|x|+|y|)^{M+1} \big)$ at the origin,
(2) the system with Hamiltonian $H+F$ is completely integrable in ${\mathbb{R}}^{2n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06626 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integrable perturbations of polynomial Hamiltonian systems Treschev, Dmitry Dynamical Systems Mathematical Physics 37J40 We consider a Hamiltonian system on the symplectic space $({\mathbb{R}}^{2n}, dy\wedge dx)$ with a real-analytic Hamiltonian $H : {\mathbb{R}}^{2n}\to {\mathbb{R}}$. We assume that the system has a non-degenerate equilibrium position at the origin. Under some nonresonance assumptions we prove the following. For any positive integer $M$ there exists a real-analytic function $F:{\mathbb{R}}^{2n}\to{\mathbb{R}}$ such that (1) $F = O\big( (|x|+|y|)^{M+1} \big)$ at the origin, (2) the system with Hamiltonian $H+F$ is completely integrable in ${\mathbb{R}}^{2n}$. |
| title | Integrable perturbations of polynomial Hamiltonian systems |
| topic | Dynamical Systems Mathematical Physics 37J40 |
| url | https://arxiv.org/abs/2605.06626 |