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Lobe dynamics and escape from a potential well are general frameworksintroduced to study phase space transport in chaotic dynamical systems. Whilethe former approach studies how regions of phase space are transported byreducing the flow to a two-dimensional map, the latter approach studies thephase space structures that lead to critical events by crossing periodic orbitaround saddles. Both of these frameworks require computation with curvesrepresented by millions of points-computing intersection points between thesecurves and area bounded by the segments of these curves-for quantifying thetransport and escape rate. We present a theory for computing these intersectionpoints and the area bounded between the segments of these curves based on aclassification of the intersection points using equivalence class. We alsopresent an alternate theory for curves with nontransverse intersections and amethod to increase the density of points on the curves for locating theintersection points accurately.The numerical implementation of the theorypresented herein is available as an open source software called Lober. We usedthis package to demonstrate the application of the theory to lobe dynamics thatarises in fluid mechanics, and rate of escape from a potential well that arisesin ship dynamics.

Computational Method for Phase Space Transport with Applications to Lobe Dynamics and Rate of Escape