Dynamical aspects of multi-round horseshoe-shaped homoclinic orbits in the RTBP

E. Barrabés; J. M. Mondelo; M. Ollé

doi:10.1007/s10569-009-9190-9

Dynamical aspects of multi-round horseshoe-shaped homoclinic orbits in the RTBP

E. Barrabés, J. M. Mondelo, M. Ollé

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

7 Citations (Scopus)

Abstract

We consider the planar restricted three-body problem and the collinear equilibrium point L3, as an example of a center×saddle equilibrium point in a Hamiltonian with two degrees of freedom. We explore numerically the existence of symmetric and non-symmetric homoclinic orbits to L3, when varying the mass parameter μ. Concerning the symmetric homoclinic orbits (SHO), we study the multi-round, m-round, SHO for m ≥ 2. More precisely, given a transversal value of μ for which there is a 1-round SHO, say μ1, we show that for any m ≥ 2, there are countable sets of values of μ, tending to μ1, corresponding to m-round SHO. Some comments on related analytical results are also made. © Springer Science+Business Media B.V. 2009.

Original language	English
Pages (from-to)	197-210
Journal	Celestial Mechanics and Dynamical Astronomy
Volume	105
Issue number	1
DOIs	https://doi.org/10.1007/s10569-009-9190-9
Publication status	Published - 1 Oct 2009

Keywords

Homoclinic connection to L3
Invariant manifolds
Multi-round homoclinic orbits
Restricted three-body problem
Symmetric homoclinic orbits

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title = "Dynamical aspects of multi-round horseshoe-shaped homoclinic orbits in the RTBP",

abstract = "We consider the planar restricted three-body problem and the collinear equilibrium point L3, as an example of a center×saddle equilibrium point in a Hamiltonian with two degrees of freedom. We explore numerically the existence of symmetric and non-symmetric homoclinic orbits to L3, when varying the mass parameter μ. Concerning the symmetric homoclinic orbits (SHO), we study the multi-round, m-round, SHO for m ≥ 2. More precisely, given a transversal value of μ for which there is a 1-round SHO, say μ1, we show that for any m ≥ 2, there are countable sets of values of μ, tending to μ1, corresponding to m-round SHO. Some comments on related analytical results are also made. {\textcopyright} Springer Science+Business Media B.V. 2009.",

keywords = "Homoclinic connection to L3, Invariant manifolds, Multi-round homoclinic orbits, Restricted three-body problem, Symmetric homoclinic orbits",

author = "E. Barrab{\'e}s and Mondelo, {J. M.} and M. Oll{\'e}",

year = "2009",

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doi = "10.1007/s10569-009-9190-9",

language = "English",

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journal = "Celestial Mechanics and Dynamical Astronomy",

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TY - JOUR

T1 - Dynamical aspects of multi-round horseshoe-shaped homoclinic orbits in the RTBP

AU - Barrabés, E.

AU - Mondelo, J. M.

AU - Ollé, M.

PY - 2009/10/1

Y1 - 2009/10/1

N2 - We consider the planar restricted three-body problem and the collinear equilibrium point L3, as an example of a center×saddle equilibrium point in a Hamiltonian with two degrees of freedom. We explore numerically the existence of symmetric and non-symmetric homoclinic orbits to L3, when varying the mass parameter μ. Concerning the symmetric homoclinic orbits (SHO), we study the multi-round, m-round, SHO for m ≥ 2. More precisely, given a transversal value of μ for which there is a 1-round SHO, say μ1, we show that for any m ≥ 2, there are countable sets of values of μ, tending to μ1, corresponding to m-round SHO. Some comments on related analytical results are also made. © Springer Science+Business Media B.V. 2009.

AB - We consider the planar restricted three-body problem and the collinear equilibrium point L3, as an example of a center×saddle equilibrium point in a Hamiltonian with two degrees of freedom. We explore numerically the existence of symmetric and non-symmetric homoclinic orbits to L3, when varying the mass parameter μ. Concerning the symmetric homoclinic orbits (SHO), we study the multi-round, m-round, SHO for m ≥ 2. More precisely, given a transversal value of μ for which there is a 1-round SHO, say μ1, we show that for any m ≥ 2, there are countable sets of values of μ, tending to μ1, corresponding to m-round SHO. Some comments on related analytical results are also made. © Springer Science+Business Media B.V. 2009.

KW - Homoclinic connection to L3

KW - Invariant manifolds

KW - Multi-round homoclinic orbits

KW - Restricted three-body problem

KW - Symmetric homoclinic orbits

U2 - 10.1007/s10569-009-9190-9

DO - 10.1007/s10569-009-9190-9

M3 - Article

VL - 105

SP - 197

EP - 210

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

IS - 1

ER -