Fractal basin boundaries and escape dynamics in a multiwell potential

TL;DR

This study investigates escape dynamics and fractal basin boundaries in a multiwell potential, revealing how initial conditions influence escape times and the coexistence of non-escaping and escaping orbits.

Contribution

It provides a detailed numerical analysis of escape basins, escape times, and fractal structures in a multiwell potential system, enhancing understanding of escape mechanisms in Hamiltonian dynamics.

Findings

Regions of non-escaping motion coexist with escape basins.

Longer escape periods occur near fractal basin boundaries.

Escape rates are lowest for initial conditions inside escape basins.

Abstract

The escape dynamics in a two-dimensional multiwell potential is explored. A thorough numerical investigation is conducted in several types of two-dimensional planes and also in a three-dimensional subspace of the entire four-dimensional phase space in order to distinguish between non-escaping (ordered and chaotic) and escaping orbits. The determination of the location of the basins of escape towards the different escape channels and their correlations with the corresponding escape time of the orbits is undoubtedly an issue of paramount importance. It was found that in all examined cases regions of non-escaping motion coexist with several basins of escape. Furthermore, we monitor how the percentages of all types of orbits evolve when the total orbital energy varies. The larger escape periods have been measured for orbits with initial conditions in the fractal basin boundaries, while the lowest escape rates belong to orbits with initial conditions inside the basins of escape. The Newton-Raphson basins of attraction of the equilibrium points of the system have also been determined. We hope that our numerical analysis will be useful for a further understanding of the escape mechanism of orbits in open Hamiltonian systems with two degrees of freedom.