Nonlinear Classical Dynamics and Knot Invariants

Based on certain analogies between Jones knot invariant and KAM theorem, it is conjectured that a generic D3 nonlinear dynamical set will evolve towards a state corresponding to a four dimensional central manifold M4 with signature τ equal to the inverse of the index [M:N]=1/φ3, where 1/φ3 is the Subtle Mean and is the Golden Mean. It is further conjectured that this selfsimilar transfinite four manifolds marks the critical limit for the onset of global chaos.