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

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

1998-01-14

arxiv.org/abs/chao-dyn/9801019v1

Physica D 99 (1996) 237-251

Nonlinear Sciences

Chaotic Dynamics

22 pages LaTeX, uses espart.sty and equation.sty

Scientific paper

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 $R^3$ as well as its constrained version referring to the generalized spherical pendulum are shown to exhibit global Hopf bifurcation.

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