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Hierarchies of similarity symmetries and singularity analysis

  • Dynamical Systems
  • Conference paper
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Dynamical Systems, Plasmas and Gravitation

Part of the book series: Lecture Notes in Physics ((LNP,volume 518))

Abstract

The singularity analysis of ordinary differential equations is based on the concept of the balance of the dominant terms. The equivalence of these terms is reflected by the possession of the same similarity symmetry. Different possible singular behaviours are reflected by different similarity symmeties. Hierarchal structures are observed. The generalised Chazy equation provides a simple example of this structure. The singularity analysis is based on the recently introduced ‘g function’ method.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Natal, 4041, Durban, South Africa

    Peter G. L. Leach

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  1. Peter G. L. Leach
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P. G. L. Leach S. E. Bouquet J.-L. Rouet E. Fijalkow

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© 1999 Springer-Verlag

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Leach, P.G.L. (1999). Hierarchies of similarity symmetries and singularity analysis. In: Leach, P.G.L., Bouquet, S.E., Rouet, JL., Fijalkow, E. (eds) Dynamical Systems, Plasmas and Gravitation. Lecture Notes in Physics, vol 518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105935

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  • DOI: https://doi.org/10.1007/BFb0105935

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65467-4

  • Online ISBN: 978-3-540-49251-1

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