Phase Space Geometry and Chaotic Attractors in Dissipative Nambu Mechanics

Details Phase Space Geometry and Chaotic Attractors in Dissipative Nambu Mechanics Phase Space Geometry and Chaotic Attractors in Dissipative Nambu Mechanics

2011-10-04

arxiv.org/abs/1110.0766v3

J. Phys. A: Math. Theor. 45 (2012) 195101

Nonlinear Sciences

Chaotic Dynamics

22 pages, 13 figures

Scientific paper

10.1088/1751-8113/45/19/195101

Following the Nambu mechanics framework we demonstrate that the non-dissipative part of the Lorenz system can be generated by the intersection of two quadratic surfaces that form a doublet under the group SL(2,R). All manifolds are classified into four dinstict classes; parabolic, elliptical, cylindrical and hyperbolic. The Lorenz attractor is localized by a specific infinite set of one parameter family of these surfaces. The different classes correspond to different physical systems. The Lorenz system is identified as a charged rigid body in a uniform magnetic field with external torque and this system is generalized to give new strange attractors.

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