A note on a conjecture of Poincaré

Gerard Gómez; Jaume Llibre

doi:https://doi.org/10.1007/BF01230393

A note on a conjecture of Poincaré

Gerard Gómez, Jaume Llibre

Department of Mathematics

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

5 Citations (Scopus)

Abstract

We prove the following weakened version of Poincaré's conjecture on the density of periodic orbits of the restricted three-body problem: The measure of Lebesgue of the set of bounded orbits which are not contained in the closure of the set of periodic orbits goes to zero when the mass parameter does. © 1981 D. Reidel Publishing Co.

Original language	English
Pages (from-to)	335-343
Journal	Celestial mechanics
Volume	24
DOIs	https://doi.org/10.1007/BF01230393
Publication status	Published - 1 Aug 1981

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title = "A note on a conjecture of Poincar{\'e}",

abstract = "We prove the following weakened version of Poincar{\'e}'s conjecture on the density of periodic orbits of the restricted three-body problem: The measure of Lebesgue of the set of bounded orbits which are not contained in the closure of the set of periodic orbits goes to zero when the mass parameter does. {\textcopyright} 1981 D. Reidel Publishing Co.",

author = "Gerard G{\'o}mez and Jaume Llibre",

year = "1981",

month = aug,

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doi = "https://doi.org/10.1007/BF01230393",

language = "English",

volume = "24",

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T1 - A note on a conjecture of Poincaré

AU - Gómez, Gerard

AU - Llibre, Jaume

PY - 1981/8/1

Y1 - 1981/8/1

N2 - We prove the following weakened version of Poincaré's conjecture on the density of periodic orbits of the restricted three-body problem: The measure of Lebesgue of the set of bounded orbits which are not contained in the closure of the set of periodic orbits goes to zero when the mass parameter does. © 1981 D. Reidel Publishing Co.

AB - We prove the following weakened version of Poincaré's conjecture on the density of periodic orbits of the restricted three-body problem: The measure of Lebesgue of the set of bounded orbits which are not contained in the closure of the set of periodic orbits goes to zero when the mass parameter does. © 1981 D. Reidel Publishing Co.

U2 - https://doi.org/10.1007/BF01230393

DO - https://doi.org/10.1007/BF01230393

M3 - Article

VL - 24

SP - 335

EP - 343

ER -

A note on a conjecture of Poincaré

Abstract

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