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Nonplanar Second Species Periodic and Chaotic Trajectories for the Circular Restricted Three-Body Problem |
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| Authors: | S Bolotin R S MacKay |
| Institution: | (1) Department of Mathematics and Moscow Steklov Mathematical Institute, University of Wisconsin-Madison, VanVleck Hall, 480 Lincoln Drive Madison, Wisconsin, 53706, USA;(2) Department of Mathematics, University of Warwick, Coventry, UK |
| Abstract: | For the circular restricted three-body problem of celestial mechanics with small secondary mass, we prove the existence of uniformly hyperbolic invariant sets of non-planar periodic and chaotic almost collision orbits. Poincaré conjectured existence of periodic ones and gave them the name “second species solutions”. We obtain large subshifts of finite type containing solutions of this type. |
| Keywords: | Collisions Regularization Second species orbits Singular perturbation Three-body problem |
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