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Block Regularisation of the Logarithm Central Force Problem

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Abstract

The logarithm function is the gravitational potential in \({\mathbb {R}}^2\). We prove that the logarithm central force problem is block regularizable, that is, the (incomplete) flow may be continuously extended over the singularity at the origin after an appropriate re-parametrization.

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Funding

This work was partially supported by a NSERC Discovery Grant.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

    Archishman Saha

  2. Department of Mathematics, Wilfrid Laurier University, Waterloo, N2L 3C5, Canada

    Cristina Stoica

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  1. Archishman Saha
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  2. Cristina Stoica
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The authors contributed equally to this work.

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Correspondence to Cristina Stoica.

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Saha, A., Stoica, C. Block Regularisation of the Logarithm Central Force Problem. J Dyn Diff Equat (2023). https://doi.org/10.1007/s10884-023-10314-x

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  • DOI: https://doi.org/10.1007/s10884-023-10314-x

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