A model for separatrix splitting near multiple resonances

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dc.creatorRudnev, M.
dc.creatorTen, V.
dc.date2005-01-13
dc.date.accessioned2026-07-07T05:16:03Z
dc.date.available2026-07-07T05:16:03Z
dc.descriptionWe propose a model for local dynamics of a perturbed convex real-analytic Liouville-integrable Hamiltonian system near a resonance of multiplicity $1+m, m\geq 0$. Physically, the model represents a toroidal pendulum, coupled with a Liouville-integrable system of $n$ non-linear rotators via a small analytic potential. The global bifurcation problem is set-up for the $n$-dimensional isotropic manifold, corresponding to a specific homoclinic orbit of the toroidal pendulum. The splitting of this manifold can be described by a scalar function on an $n$-torus, whose $k$th Fourier coefficient satisfies the estimate $$O(e^{- ρ|k\cdotω| - |k|σ}), k\in\Z^n\setminus\{0\},$$ where $ω\in\R^n$ is a Diophantine rotation vector of the system of rotators; $ρ\in(0,{π\over2})$ and $σ>0$ are the analyticity parameters built into the model. The estimate, under suitable assumptions would generalize to a general multiple resonance normal form of a convex analytic Liouville integrable Hamiltonian system, perturbed by $O(\eps)$, in which case $ω_j\sim\omeps, j=1,...,n.$
dc.description24 pages
dc.identifierhttps://arxiv.org/abs/math/0501208
dc.identifierhttp://arxiv.org/abs/math/0501208
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73847
dc.subjectDynamical Systems
dc.subjectMathematical Physics
dc.subject70H08; 70H20
dc.titleA model for separatrix splitting near multiple resonances
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