Hamilton-Jacobi method for a simple resonance
| dc.creator | Rudnev, Mischa | |
| dc.date | 2003-05-09 | |
| dc.date.accessioned | 2026-07-07T04:57:52Z | |
| dc.date.available | 2026-07-07T04:57:52Z | |
| dc.description | It is well known that a generic small perturbation of a Liouville-integrable Hamiltonian system causes breakup of resonant and near-resonant invariant tori. A general approach to the simple resonance case in the convex real-analytic setting is developed, based on a new technique for solving the Hamilton-Jacobi equation. It is shown that a generic perturbation creates in the core of a resonance a partially hyperbolic lower-dimensional invariant torus, whose Lagrangian stable and unstable manifolds, described as global solutions of the Hamilton-Jacobi equation, split away from this torus at exponentially small angles. Optimal upper bounds with best constants are obtained for exponentially small splitting in the general case. | |
| dc.description | 40 pages | |
| dc.identifier | https://arxiv.org/abs/math/0305143 | |
| dc.identifier | http://arxiv.org/abs/math/0305143 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67417 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Mathematical Physics | |
| dc.subject | 37J40; 37J45 | |
| dc.title | Hamilton-Jacobi method for a simple resonance | |
| dc.type | text |