Characterization of transversal homothetic solutions in the n-body problem

Carles Simó; Jaume Llibre

doi:https://doi.org/10.1007/BF00250623

Characterization of transversal homothetic solutions in the n-body problem

Carles Simó, Jaume Llibre

Department of Mathematics

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

11 Citations (Scopus)

Abstract

Homothetic solutions of the n-body problem can be seen as heteroclinic orbits when the dynamical variables are changed via the McGehee blow-up and the time is suitably scaled. Transversality of the invariant asymptotic manifolds which contain the heteroclinic orbits is related to some structural stability. We fully characterize the cases in which such transversality is obtained for the n-body problem in any dimension. © 1981 Springer-Verlag GmbH & Co.

Original language	English
Pages (from-to)	189-198
Journal	Archive for Rational Mechanics and Analysis
Volume	77
DOIs	https://doi.org/10.1007/BF00250623
Publication status	Published - 1 Jun 1981

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title = "Characterization of transversal homothetic solutions in the n-body problem",

abstract = "Homothetic solutions of the n-body problem can be seen as heteroclinic orbits when the dynamical variables are changed via the McGehee blow-up and the time is suitably scaled. Transversality of the invariant asymptotic manifolds which contain the heteroclinic orbits is related to some structural stability. We fully characterize the cases in which such transversality is obtained for the n-body problem in any dimension. {\textcopyright} 1981 Springer-Verlag GmbH & Co.",

author = "Carles Sim{\'o} and Jaume Llibre",

year = "1981",

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T1 - Characterization of transversal homothetic solutions in the n-body problem

AU - Simó, Carles

AU - Llibre, Jaume

PY - 1981/6/1

Y1 - 1981/6/1

N2 - Homothetic solutions of the n-body problem can be seen as heteroclinic orbits when the dynamical variables are changed via the McGehee blow-up and the time is suitably scaled. Transversality of the invariant asymptotic manifolds which contain the heteroclinic orbits is related to some structural stability. We fully characterize the cases in which such transversality is obtained for the n-body problem in any dimension. © 1981 Springer-Verlag GmbH & Co.

AB - Homothetic solutions of the n-body problem can be seen as heteroclinic orbits when the dynamical variables are changed via the McGehee blow-up and the time is suitably scaled. Transversality of the invariant asymptotic manifolds which contain the heteroclinic orbits is related to some structural stability. We fully characterize the cases in which such transversality is obtained for the n-body problem in any dimension. © 1981 Springer-Verlag GmbH & Co.

U2 - https://doi.org/10.1007/BF00250623

DO - https://doi.org/10.1007/BF00250623

M3 - Article

VL - 77

SP - 189

EP - 198

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

ER -

Characterization of transversal homothetic solutions in the n-body problem

Abstract

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