Affiliation:
1. Mathematisch Instituut, P. O. Box 80.010, 3508TA Utrecht, Netherlands
Abstract
In a neighborhood of stable equilibrium, we consider the dynamics for at least three degrees-of-freedom (dof) Hamiltonian systems (2 dof systems are not ergodic in this case). A complication is that the recurrence properties depend strongly on the resonances of the corresponding linearized system and on quasi-trapping. In contrast to the classical FPU-chain, the inhomogeneous FPU-chain shows nearly all the principal resonances. Using this fact, we construct a periodic FPU-chain of low dimension, called a FPU-cell. Such a cell can be used as a building block for a chain of FPU-cells, called a cell-chain. Recurrence phenomena depend strongly on the physical assumptions producing specific Hamiltonians; we demonstrate this for the [Formula: see text] resonance, both general and for the FPU case; this resonance shows dynamics on different timescales. In addition we will study the relations and recurrence differences between several FPU-cells and a few cell-chains in the case of the classical near-integrable FPU-cell and of chaotic cells in [Formula: see text] resonance.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Hamiltonian Resonances;Surveys and Tutorials in the Applied Mathematical Sciences;2023
2. Variations on the Fermi-Pasta-Ulam Chain, a Survey;13th Chaotic Modeling and Simulation International Conference;2021
3. Henri Poincaré's neglected ideas;Discrete & Continuous Dynamical Systems - S;2020
4. Recurrence and Resonance in the Cubic Klein-Gordon Equation;Acta Applicandae Mathematicae;2019-01-23
5. Interaction of Lower and Higher Order Hamiltonian Resonances;International Journal of Bifurcation and Chaos;2018-07