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Numerical continuation of families of heteroclinic connections between periodic orbits in a Hamiltonian system

This paper is devoted to the numerical computation and continuation of families of heteroclinic connections between hyperbolic periodic orbits (POs) of a Hamiltonian system. We describe a method that requires the numerical continuation of a nonlinear system that involves the initial conditions of the two POs, the linear approximations of the corresponding manifolds and a point in a given Poincaré section where the unstable and stable manifolds match. The method is applied to compute families of heteroclinic orbits between planar Lyapunov POs around the collinear equilibrium points of the restricted three-body problem in different scenarios. In one of them, for the Sun-Jupiter mass parameter, we provide energy ranges for which the transition between different resonances is possible

© Nonlinearity, 2013, vol. 26, núm. 10, p. 2747-2765

IOP Publishing

Author: Barrabés Vera, Esther
Mondelo, Josep M.
Ollé Torner, Mercè
Date: 2013 October 1
Abstract: This paper is devoted to the numerical computation and continuation of families of heteroclinic connections between hyperbolic periodic orbits (POs) of a Hamiltonian system. We describe a method that requires the numerical continuation of a nonlinear system that involves the initial conditions of the two POs, the linear approximations of the corresponding manifolds and a point in a given Poincaré section where the unstable and stable manifolds match. The method is applied to compute families of heteroclinic orbits between planar Lyapunov POs around the collinear equilibrium points of the restricted three-body problem in different scenarios. In one of them, for the Sun-Jupiter mass parameter, we provide energy ranges for which the transition between different resonances is possible
Format: application/pdf
ISSN: 0951-7715 (versió paper)
1361-6544 (versió electrònica)
Document access: http://hdl.handle.net/10256/12690
Language: eng
Publisher: IOP Publishing
Collection: Versió preprint del document publicat a: http://dx.doi.org/10.1088/0951-7715/26/10/2747
Articles publicats (D-IMA)
Is part of: © Nonlinearity, 2013, vol. 26, núm. 10, p. 2747-2765
Rights: Tots els drets reservats
Subject: Anàlisi numèrica
Numerical analysis
Planetes -- Òrbites
Planets -- Orbits
Dinàmica estel·lar
Stellar dynamics
Mecànica celest
Celestial mechanics
Sistemes hamiltonians
Hamiltonian systems
Sistemes dinàmics diferenciables
Differentiable dynamical systems
Title: Numerical continuation of families of heteroclinic connections between periodic orbits in a Hamiltonian system
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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