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

Roberto Castelli*, Susanna Terracini

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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 ow, where collision solutions are replaced with transmission trajectories, is continuous, though not differentiable, with respect to the initial data.

Original languageEnglish
Pages (from-to)1197-1218
Number of pages22
JournalDiscrete and Continuous Dynamical Systems
Volume31
Issue number4
DOIs
Publication statusPublished - Dec 2011

Keywords

  • Logarithmic potential
  • Regularization technique
  • Two-body problem
  • Weak singular potential

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