On the centre manifold of collinear points in the planar three-body problem

Regina Martínez; Anna Samà

doi:https://doi.org/10.1023/A:1022901808349

On the centre manifold of collinear points in the planar three-body problem

Regina Martínez, Anna Samà

Department of Mathematics

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

3 Citations (Scopus)

Abstract

We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.

Original language	English
Pages (from-to)	311-340
Journal	Celestial Mechanics and Dynamical Astronomy
Volume	85
DOIs	https://doi.org/10.1023/A:1022901808349
Publication status	Published - 1 Apr 2003

Keywords

Homographic solutions
KAM theory
Libration points
Three-body problem

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abstract = "We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.",

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AU - Samà, Anna

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N2 - We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.

AB - We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.

KW - Homographic solutions

KW - KAM theory

KW - Libration points

KW - Three-body problem

U2 - https://doi.org/10.1023/A:1022901808349

DO - https://doi.org/10.1023/A:1022901808349

M3 - Article

VL - 85

SP - 311

EP - 340

JO - Celestial Mechanics and Dynamical Astronomy

JF - Celestial Mechanics and Dynamical Astronomy

SN - 0923-2958

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