Symplectic integration of deviation vectors and chaos determination. Application to the Hénon-Heiles model and to the restricted three-body problem

Abstract

In this work we propose a new numerical approach to distinguish between regular and chaotic orbits in Hamiltonian systems, based on the simultaneous integration of both the orbit and the deviation vectors using a symplectic scheme, hereby called {\em global symplectic integrator}. In particular, the proposed method allows us to recover the correct orbits character with very large integration time steps, small energy losses and short CPU times. To illustrate the numerical performances of the global symplectic integrator we will apply it to two well-known and widely studied problems: the Hénon-Heiles model and the restricted three-body problem.

References in corpus (2)

• Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi--Pasta--Ulam lattices by the Generalized Alignment Index method
• Improving beam stability in particle accelerator models by using Hamiltonian control

Cited by in corpus (2)

• Comparing the efficiency of numerical techniques for the integration of variational equations
• On the use of the MEGNO indicator with the Global Symplectic Integrator