The Kepler Problem with Anisotropic Perturbations

Details The Kepler Problem with Anisotropic Perturbations The Kepler Problem with Anisotropic Perturbations

2009-09-27

arxiv.org/abs/0909.4906v1

J. Math. Phys. 46, 072701 (2005)

Physics

Mathematical Physics

Scientific paper

10.1063/1.1952580

We study a 2-body problem given by the sum of the Newtonian potential and an anisotropic perturbation that is a homogeneous function of degree $-\beta$, $\beta\ge 2$. For $\beta>2$, the sets of initial conditions leading to collisions/ejections and the one leading to escapes/captures have positive measure. For $\beta>2$ and $\beta\ne 3$, the flow on the zero-energy manifold is chaotic. For $\beta=2$, a case we prove integrable, the infinity manifold of the zero-energy level is a disconnected set, which has heteroclinic connections with the collision manifold.

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