Nonplanar Second Species Periodic and Chaotic Trajectories for the Circular Restricted Three-Body Problem

Details Nonplanar Second Species Periodic and Chaotic Trajectories for the Circular Restricted Three-Body Problem Nonplanar Second Species Periodic and Chaotic Trajectories for the Circular Restricted Three-Body Problem

Apr 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006cemda..94..433b&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 94, Issue 4, pp.433-449

Astronomy and Astrophysics

Astronomy

4

Collisions, Regularization, Second Species Orbits, Singular Perturbation, Three-Body Problem

Scientific paper

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.

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