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

Abstract

Lobe dynamics and escape from a potential well are general frameworks introduced to study phase space transport in chaotic dynamical systems. While the former approach studies how regions of phase space are transported by reducing the flow to a two-dimensional map, the latter approach studies the phase space structures that lead to critical events by crossing periodic orbit around saddles. Both of these frameworks require computation with curves represented by millions of points-computing intersection points between these curves and area bounded by the segments of these curves-for quantifying the transport and escape rate. We present a theory for computing these intersection points and the area bounded between the segments of these curves based on a classification of the intersection points using equivalence class. We also present an alternate theory for curves with nontransverse intersections and a method to increase the density of points on the curves for locating the intersection points accurately.The numerical implementation of the theory presented herein is available as an open source software called Lober. We used this package to demonstrate the application of the theory to lobe dynamics that arises in fluid mechanics, and rate of escape from a potential well that arises in ship dynamics.

33 pages, 17 figures

References in corpus (2)

• Fractal basin boundaries and escape dynamics in a multiwell potential
• Escape dynamics and fractal basins boundaries in the three-dimensional Earth-Moon system

Cited by in corpus (5)

• Geometry of escape and transition dynamics in the presence of dissipative and gyroscopic forces in two degree of freedom systems
• Classical and quantum dynamical manifestations of index-2 saddles: concerted versus sequential reaction mechanisms
• Cislunar Mean-Motion Resonances: Definitions, Widths, and Comparisons with Resonant Satellites
• Designing robust trajectories by lobe dynamics in low-dimensional Hamiltonian systems
• Design of low-energy transfers in cislunar space using sequences of lobe dynamics