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On the Existence of Periodic Orbits for the Fixed Homogeneous Circle Problem

C. Azevedo·P. Ontaneda
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Abstract

We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and very near the homogeneous circle, as well as eight and spiral periodic orbits.

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C. Azevedo, P. Ontaneda. 2005-03-23. On the Existence of Periodic Orbits for the Fixed Homogeneous Circle Problem. https://arxiv.org/abs/math/0502305

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