Non Hamiltonian Chaos from Nambu Dynamics of Surfaces

• Published in: arXiv.org
• Main Author: Axenides, Minos
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 02.09.2011
• Subjects: Attractors (mathematics); Chaos theory; Cylinders; Deformation; Equations of motion; Lorenz system; Physics - Chaotic Dynamics; Physics - High Energy Physics - Theory; Strange attractors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1109.0470

We discuss recent work with E.Floratos (JHEP 1004:036,2010) on Nambu Dynamics of Intersecting Surfaces underlying Dissipative Chaos in \(R^{3}\). We present our argument for the well studied Lorenz and R\"{o}ssler strange attractors. We implement a flow decomposition to their equations of motion. Their volume preserving part preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. For dynamical systems with linear dissipative sector such as the Lorenz system, they are specified in terms of Intersecting Quadratic Surfaces. For the case of the R\"{o}ssler system, with nonlinear dissipative part, they are given in terms of a Helicoid intersected by a Cylinder. In each case they foliate the entire phase space and get deformed by Dissipation, the irrotational component to their flow. It is given by the gradient of a surface in \(R^{3}\) specified in terms of a scalar function. All three intersecting surfaces reproduce completely the dynamics of each strange attractor.