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<p>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.</p>

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Moser regularization of a stochastically perturbed Kepler problem

  • 期刊论文

  • 发表日期：

    2025年11月11日

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  • Archishman Saha

摘要

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.