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arXiv · 2504.14442

Moser Regularization of a Stochastically Perturbed Kepler Problem

Archishman Saha
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Abstract

We consider a stochastic Kepler problem perturbed by a Hamiltonian noise affecting the angular momentum vector. We show that the angular momentum and the Laplace-Runge-Lenz vectors are conserved in magnitude and as a consequence, the distance and speed of the particle follow deterministic dynamics. Further, in a procedure similar to Moser's regularization, we transform the stochastic Kepler problem to obtain its dynamics as a stochastic geodesic flow on a 3-sphere.

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Archishman Saha. 2025-04-20. Moser Regularization of a Stochastically Perturbed Kepler Problem. https://arxiv.org/abs/2504.14442

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