Abstract
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 contribution | A model for separatrix splitting near multiple resonances |
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Original language | English |
Pages (from-to) | 83 - 102 |
Number of pages | 20 |
Journal | Regular and Chaotic Dynamics |
Volume | 11 (1) |
DOIs | |
Publication status | Published - Jan 2006 |