On the regularization of the collision solutions of the one-center problem with weak forces

2009/05/11 by Castelli Roberto, Roberto, Castelli, Terracini Susanna +1
Engineering · Mathematics · Physics and Astronomy · #70F05 #70F16 #Dynamical Systems (math.DS) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Quantum chaos and dynamical systems #Spacecraft Dynamics and Control #math.DS #msc:70F05 #msc:70F16

paper · pdf · doi:10.48550/arxiv.0905.1579

21 pages, 8 figures

arxiv created 2009/05/11 · openalex publication_date 2009/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the possible regularization of collision solutions for one centre problems with a weak singularity. In the case of logarithmic singularities, we consider the method of regularization via smoothing of the potential. With this technique, we prove that the extended flow, where collision solutions are replaced with a transmission trajectory, is continuous, though not differentiable, with respect to the initial data.

Citations

• Regularization of kepler's problem and the averaging method on a manifold

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