Phase Space Geometry and Chaotic Attractors in Dissipative Nambu Mechanics

2011/10/31 by Zacharias Roupas · 1 citation
Physics and Astronomy · Mathematics · #nlin.CD #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8113/45/19/195101

published as J. Phys. A: Math. Theor. 45 (2012) 195101 · 22 pages, 13 figures

arxiv created 2012/04/25 · arxiv updated 2012/04/26

Abstract

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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• Structure preserving integration of 3D dissipative bi-Hamiltonian/Nambu systems

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