Non Hamiltonian Chaos from Nambu Dynamics of Surfaces

Abstract

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 Rössler 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 Rössler 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.

10 pages, Invited Talks at the International Conferences on: Nonlinear Dynamics and Complexity; Theory, Methods and Applications, 12-16 July 2010, Thessaloniki, Greece; Second Greek-Turkish Conference on Statistical Mechanics and Dynamical Systems, Turunc-Symi, 5-12 September 2010