KAM Theorems for Multi-scale Torus
Dynamical Systems
2023-01-03 v2
Abstract
In present paper, from the viewpoint of physical intuition we introduce a Hamiltonian system with multiscale rotation, which describes many systems, for example, the forced pendulum with fast rotation, weakly coupled -oscillators with quasiperiodic force and so on. We study the persistence of invariant tori for this Hamiltonian system, and establish some KAM type results including the isoenergetic type. As consequences, we can show that Boltzmann's ergodicity hypothesis is also not true for this Hamiltonian system.
Cite
@article{arxiv.2212.14212,
title = {KAM Theorems for Multi-scale Torus},
author = {Weichao Qian and Yixian Gao and Yong Li},
journal= {arXiv preprint arXiv:2212.14212},
year = {2023}
}
Comments
33pages