A model for separatrix splitting near multiple resonances

M Rudnev, VV Ten

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)


We propose and study a model for local dynamics of a perturbed convex real-analytic Liouville-integrable Hamiltonian system near a resonance of multiplicity 1 + m, m>/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+1 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 the n-torus. A sharp estimate for its Fourier coefficients is proven. It generalizes to a multiple resonance normal form of a convex analytic Liouville near-integrable Hamiltonian system. The bound then is exponentially small.
Translated title of the contributionA model for separatrix splitting near multiple resonances
Original languageEnglish
Pages (from-to)83 - 102
Number of pages20
JournalRegular and Chaotic Dynamics
Volume11 (1)
Publication statusPublished - Jan 2006

Bibliographical note

Publisher: Turpion


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