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We discuss recent work with E.Floratos (JHEP 1004:036,2010) on Nambu Dynamicsof Intersecting Surfaces underlying Dissipative Chaos in $R^{3}$. We presentour argument for the well studied Lorenz and R\"{o}ssler strange attractors. Weimplement a flow decomposition to their equations of motion. Their volumepreserving part preserves in time a family of two intersecting surfaces, the socalled {\em Nambu Hamiltonians}. For dynamical systems with linear dissipativesector such as the Lorenz system, they are specified in terms of IntersectingQuadratic Surfaces. For the case of the R\"{o}ssler system, with nonlineardissipative part, they are given in terms of a Helicoid intersected by aCylinder. In each case they foliate the entire phase space and get deformed byDissipation, the irrotational component to their flow. It is given by thegradient of a surface in $R^{3}$ specified in terms of a scalar function. Allthree intersecting surfaces reproduce completely the dynamics of each strangeattractor.

Non Hamiltonian Chaos from Nambu Dynamics of Surfaces