Groups and nonlinear dynamical systems. Dynamics on the SU(2) group

1998/01/14 by K. Kowalski, J. Rembielinski
Physics and Astronomy · #chao-dyn #nlin.CD

paper · pdf

published as Physica D 99 (1996) 237-251 · 22 pages LaTeX, uses espart.sty and equation.sty

arxiv created 1998/01/14 · arxiv updated 2009/11/30

Abstract

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 R³ as well as its constrained version referring to the generalized spherical pendulum are shown to exhibit global Hopf bifurcation.

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