Groups and nonlinear dynamical systems. Chaotic dynamics on the SU(2)xSU(2) group

Details Groups and nonlinear dynamical systems. Chaotic dynamics on the SU(2)xSU(2) group Groups and nonlinear dynamical systems. Chaotic dynamics on the SU(2)xSU(2) group

1998-01-14

arxiv.org/abs/chao-dyn/9801020v1

Chaos, Solitons & Fractals, 9 (1998) 437-448

Nonlinear Sciences

Chaotic Dynamics

12 pages LaTeX, uses espart.sty and equation.sty; accepted for publication in Chaos, Solitons & Fractals

Scientific paper

In our previous paper: K. Kowalski and J. Rembieli\'nski, Groups and nonlinear dynamical systems. Dynamics on the SU(2) group, Physica D 99, 237 (1996), we introduced an abstract Newton-like equation on a general Lie algebra such that submanifolds fixed by the second-order Casimir operator are attracting set. The corresponding group parameters satisfy the nonlinear dynamical system having an attractor coinciding with the submanifold. In this work we discuss the case with the $SU(2)\times SU(2)$ group. The resulting second-order system in $R^6$ is demonstrated to exhibit chaotic behaviour.

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