Singular KAM theory for convex Hamiltonian systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918094696349696 |
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| author | Barbieri, Santiago Biasco, Luca Chierchia, Luigi Zaccaria, Davide |
| author_facet | Barbieri, Santiago Biasco, Luca Chierchia, Luigi Zaccaria, Davide |
| contents | In this note, we briefly discuss how singular KAM Theory - which was worked out in a previous work by L.B. and L.C. for the mechanical case $\frac12 |y|^2+\varepsilon f(x)$ - can be extended to convex real analytic nearly integrable Hamiltonian systems with Hamiltonian in action-angle variables given by $h(y)+\varepsilon f(x)$ with $h$ convex and generic $f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12101 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singular KAM theory for convex Hamiltonian systems Barbieri, Santiago Biasco, Luca Chierchia, Luigi Zaccaria, Davide Dynamical Systems In this note, we briefly discuss how singular KAM Theory - which was worked out in a previous work by L.B. and L.C. for the mechanical case $\frac12 |y|^2+\varepsilon f(x)$ - can be extended to convex real analytic nearly integrable Hamiltonian systems with Hamiltonian in action-angle variables given by $h(y)+\varepsilon f(x)$ with $h$ convex and generic $f$. |
| title | Singular KAM theory for convex Hamiltonian systems |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2507.12101 |