D. Wilczak, P. Zgliczynski
Published 2004-01-14Version 1
We present a method for proving the existence of symmetric periodic, heteroclinic or homoclinic orbits in dynamical systems with the reversing symmetry. As an application we show that the Planar Restricted Circular Three Body Problem (PCR3BP) corresponding to the Sun-Jupiter-Oterma system possesses an infinite number of symmetric periodic orbits and homoclinic orbits to the Lyapunov orbits. Moreover, we show the existence of symbolic dynamics on six symbols for PCR3BP and the possibility of resonance transitions of the comet. This extends earlier results by Wilczak and Zgliczynski - Heteroclinic Connections between Periodic Orbits in Planar Restricted Circular Three Body Problem - A Computer Assisted Proof, Commun. Math. Phys. 234, 37-75 (2003).
Comments: 18 pages, 5 figures
Transitive decomposition of symmetry groups for the $n$-body problem
Periodic oscillations in the restricted Hip-Hop 2N+1 body problem
Bifurcation of periodic orbits for the $N$-body problem, from a non geometrical family of solutions
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