April  2006, 14(2): 235-260. doi: 10.3934/dcds.2006.14.235

Shadowing chains of collision orbits

1. 

Department of Mathematics, University of Wisconsin, Madison, United States

Received  November 2004 Revised  March 2005 Published  November 2005

We consider a Hamiltonian system modeling the plane restricted elliptic 3 body problem with one of the masses small and prove the existence of periodic and chaotic orbits shadowing chains of collision orbits. Periodic orbits of this type were first studied by Poincaré for the non-restricted 3 body problem. The present paper contains general results which hold for time periodic Hamiltonian systems with a small Newtonian singularity. Applications to celestial mechanics will be given in a subsequent paper.
Citation: Sergey V. Bolotin. Shadowing chains of collision orbits. Discrete & Continuous Dynamical Systems - A, 2006, 14 (2) : 235-260. doi: 10.3934/dcds.2006.14.235
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