Oscillatory motions in the rectangular four body problem
Ernesto A. Lacomba Mario Medina
Discrete & Continuous Dynamical Systems - S 2008, 1(4): 557-587 doi: 10.3934/dcdss.2008.1.557
In this paper we describe a symbolic dynamics for the rectangular four body problem by applying blow ups at total collisions and at infinity, studying the homoclinic or heteroclinic orbits obtained as intersection of corresponding two dimensional invariant submanifolds in a 3 dimensional energy level plus a convenient Poincaré map. With this tool we show the existence of a very rich dynamics and obtain the Main Theorem of this article. It gives the transition matrix for the symbolic dynamics of the images of conveniently chosen rectangles in the Poincaré section of the flow.
keywords: symbolic dynamics Poincaré section. Four body problem invariant manifolds

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