Escapes in Hamiltonian systems with multiple exit channels: Part I

Abstract

The aim of this work is to review and also explore even further the escape properties of orbits in a dynamical system of a two-dimensional perturbed harmonic oscillator, which is a characteristic example of open Hamiltonian systems. In particular, we conduct a thorough numerical investigation distinguishing between trapped (ordered and chaotic) and escaping orbits, considering only unbounded motion for several energy levels. It is of particular interest, to locate the basins of escape towards the different escape channels and connect them with the corresponding escape periods of the orbits. We split our examination into three different cases depending on the function of the perturbation term which determines the number of escape channels on the physical space. In every case, we computed extensive samples of orbits in both the physical and the phase space by integrating numerically the equations of motion as well as the variational equations. In an attempt to determine the regular or chaotic nature of trapped motion, we applied the SALI method as a chaos detector. It was found, that in all studied cases regions of trapped orbits coexist with several basins of escape. It was also observed, that for energy levels very close to the escape value the escape times of orbits are large, while for values of energy much higher than the escape energy the vast majority of orbits escape very quickly or even immediately to infinity. The larger escape periods have been measured for orbits with initial conditions in the boundaries of the escape basins and also in the vicinity of the fractal structure. Most of the current outcomes have been compared with previous related work. We hope that our results will be useful for a further understanding of the escape mechanism of orbits in open Hamiltonian systems with two degrees of freedom.

Published in Nonlinear Dynamics (NODY) journal. arXiv admin note: previous papers with related context: arXiv:1404.4285, arXiv:1411.4864

References in corpus (6)

• A Hamiltonian system of three degrees of freedom with eight channels of escape: The Great Escape
• Trapped and escaping orbits in an axially symmetric galactic-type potential
• Periodic Orbits and Escapes in Dynamical Systems
• Investigating the nature of motion in 3D perturbed elliptic oscillators displaying exact periodic orbits
• Application of new dynamical spectra of orbits in Hamiltonian systems
• Are semi-numerical methods an effective tool for locating periodic orbits in 3D potentials?

Cited by in corpus (20)

• Crash test for the Copenhagen problem with oblateness
• Classifying orbits in the restricted three-body problem
• Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries
• Periodic Orbit Families in the Gravitational Field of Irregular-shaped Bodies
• Fractal basin boundaries and escape dynamics in a multiwell potential
• Escapes in Hamiltonian systems with multiple exit channels: Part II
• Orbital dynamics in the planar Saturn-Titan system
• Orbital and escape dynamics in barred galaxies - I. The 2D system
• An overview of the escape dynamics in the Henon-Heiles Hamiltonian system
• Escape dynamics and fractal basins boundaries in the three-dimensional Earth-Moon system
• How does the oblateness coefficient influence the nature of orbits in the restricted three-body problem?
• Geometry of escape and transition dynamics in the presence of dissipative and gyroscopic forces in two degree of freedom systems
• Orbit classification in the Hill problem: I. The classical case
• Elucidating the escape dynamics of the four hill potential
• Comparing the escape dynamics in tidally limited star cluster models
• Investigating the planar circular restricted three-body problem with strong gravitational field
• Ergodic decay laws in Newtonian and relativistic chaotic scattering
• Escape dynamics and fractal basin boundaries in Seyfert galaxies
• Escape dynamics in a binary system of interacting galaxies
• Fugitive stars in active galaxies