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Singularities of Implicit Differential Equations and Static Bifurcations

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Computer Algebra in Scientific Computing (CASC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8136))

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Abstract

We discuss geometric singularities of implicit ordinary differential equations from the point of view of Vessiot theory. We show that quasi-linear systems admit a special treatment leading to phenomena not present in the general case. These results are then applied to study static bifurcations of parametric ordinary differential equations.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Kassel, 34132, Kassel, Germany

    Werner M. Seiler

Authors
  1. Werner M. Seiler
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Editor information

Editors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Moscow Region, Russia

    Vladimir P. Gerdt

  2. Institut für Mathematik, Universität Kassel, Heinrich-Plett-Straße 40, 34132, Kassel, Germany

    Wolfram Koepf

  3. Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr

  4. Khristianovich Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Seiler, W.M. (2013). Singularities of Implicit Differential Equations and Static Bifurcations. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_29

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  • DOI: https://doi.org/10.1007/978-3-319-02297-0_29

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02296-3

  • Online ISBN: 978-3-319-02297-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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