Dynamics of nonlinear resonances in Hamiltonian systems
arXiv:0805.0358 · doi:10.1209/0295-5075/85/14004
Abstract
It is well known that the dynamics of a Hamiltonian system depends crucially on whether or not it possesses nonlinear resonances. In the generic case, the set of nonlinear resonances consists of independent clusters of resonantly interacting modes, described by a few low-dimensional dynamical systems. We show that 1) most frequently met clusters are described by integrable dynamical systems, and 2) construction of clusters can be used as the base for the Clipping method, substantially more effective for these systems than the Galerkin method. The results can be used directly for systems with cubic Hamiltonian.
New version: improved physical motivation and added details about clipping method
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- Finite-Dimensional Turbulence of Planetary Waves
- Externally forced triads of resonantly interacting waves: boundedness and integrability properties
- Complete classification of discrete resonant Rossby/drift wave triads on periodic domains
- Quadratic invariants for discrete clusters of weakly interacting waves
- Percolation transition in the kinematics of nonlinear resonance broadening in Charney-Hasegawa-Mima model of Rossby wave turbulence
- Nonlinear resonances of water waves
- On the time-evolution of resonant triads in rotational capillary-gravity water waves
- Discrete wave turbulence of rotational capillary water waves
- The hidden role of coupled wave network topology on the dynamics of nonlinear lattices