Groups and nonlinear dynamical systems. Dynamics on the SU(2) group
chao-dyn
2007-05-23 v1 混沌动力学
摘要
An abstract Newton-like equation on a general Lie algebra is introduced such that orbits of the Lie-group action are attracting set. This equation generates the nonlinear dynamical system satisfied by the group parameters having an attractor coinciding with the orbit. The periodic solutions of the abstract equation on a Lie algebra are discussed. The particular case of the SU(2) group is investigated. The resulting nonlinear second-order dynamical system in as well as its constrained version referring to the generalized spherical pendulum are shown to exhibit global Hopf bifurcation.
引用
@article{arxiv.chao-dyn/9801019,
title = {Groups and nonlinear dynamical systems. Dynamics on the SU(2) group},
author = {K. Kowalski and J. Rembielinski},
journal= {arXiv preprint arXiv:chao-dyn/9801019},
year = {2007}
}
备注
22 pages LaTeX, uses espart.sty and equation.sty