|
Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
A model for separatrix splitting near multiple resonances
M. Rudnev, V. Ten Department of Mathematics,
University of Bristol,
University Walk, Bristol BS8 1TW, UK
Аннотация:
We propose and study a model for local dynamics of a perturbed convex real-analytic Liouville-integrable Hamiltonian system near a resonance of multiplicity $1+m$, $m \geqslant 0$. 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.
Ключевые слова:
near-integrable Hamiltonian systems, resonances, splitting of separatrices.
Поступила в редакцию: 30.05.2005 Принята в печать: 25.11.2005
Образец цитирования:
M. Rudnev, V. Ten, “A model for separatrix splitting near multiple resonances”, Regul. Chaotic Dyn., 11:1 (2006), 83–102
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd659 https://www.mathnet.ru/rus/rcd/v11/i1/p83
|
|