Quasi‐Periodic Almost‐Collision Orbits in the Spatial Three‐Body Problem |
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| Authors: | Lei Zhao |
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| Affiliation: | Johann Bernoulli Institute for Mathematics and Computer Science Rijksuniversiteit Groningen, AG, Groningen, Netherlands |
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| Abstract: | 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. |
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