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

Roberto Castelli; Susanna Terracini

doi:10.3934/dcds.2011.31.1197

Article Contents

2011, Volume 31, Issue 4: 1197-1218. Doi: 10.3934/dcds.2011.31.1197

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

Roberto Castelli^1, and
Susanna Terracini^2,

1.
BCAM - Basque Center for Applied Mathematics, Bizkaia Technology Park, 48160 Derio, Bizkaia,
2.
Università di Milano Bicocca, Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125 Milano

Received: December 31, 2009

Revised: February 28, 2010

Published: September 2011

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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 transmission trajectories, is continuous, though not differentiable, with respect to the initial data.

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Mathematics Subject Classification: Primary: 70F16, 70F35; Secondary: 34H45.

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