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Quasi‐Periodic Almost‐Collision Orbits in the Spatial Three‐Body Problem
Author(s) -
Zhao Lei
Publication year - 2015
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21539
Subject(s) - limit (mathematics) , mathematics , planar , three body problem , periodic orbits , collision , zero (linguistics) , mathematical analysis , set (abstract data type) , measure (data warehouse) , pure mathematics , classical mechanics , physics , computer science , linguistics , philosophy , computer graphics (images) , computer security , database , programming language
In a system of particles, quasi‐periodic almost‐collision orbits are collisionless orbits along which two bodies become arbitrarily close to each other—the lower limit of their distance is zero but the upper limit is strictly positive—and are quasi‐periodic in a regularized system up to a change of time. Their existence was shown in the restricted planar circular three‐body problem by A.~Chenciner and J. Llibre, and in the planar three‐body problem by J. Féjoz. In the spatial three‐body problem, the existence of a set of positive measure of such orbits was predicted by C. Marchal. In this article, we present a proof of this fact.© 2015 Wiley Periodicals, Inc.