A New Frame for Phase Space Analysis

Abstract: In this talk, we introduce a new change of coordinates,  which we term Local Orthogonal Rectification, or LOR, that can be applied at any selected curve in the phase space of a dynamical system.  We use the LOR approach to derive a novel definition for rivers, long-recognized but poorly understood trajectories that locally attract other orbits yet need not be related to invariant manifolds or other familiar phase space structures, and to identify rivers within several example systems.  We also apply the LOR approach to locate periodic orbits in higher dimensional flows, and identify a new type of invariant manifold attendant to some limit cycles.