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Japan Journal of Applied Mathematics

, Volume 4, Issue 3, pp 393–431 | Cite as

Constrained systems, characteristic surfaces, and normal forms

  • Hiroe Oka
Article

Abstract

ODEs with a small parameter ε multiplying derivatives, which have been studied as a singular perturbation problem, are formulated in a coordinate-free manner, as a pair of a vector field and a tensor field, in order to treat them as a bifurcation problem. This formulation is an extension of the classical interpretation of autonomous ODEs as vector fields, and it is called a constrained system. A method to obtain normal forms for constrained systems is given as well as several results of computing them. Unfoldings of these normal forms include a large part of typical behaviors observed in such ODEs with ε. The local classification of characteristic surfaces is also discussed.

Key words

constrained system characteristic surface normal form singular perturbation bifurcation 

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Copyright information

© JJAM Publishing Committee 1987

Authors and Affiliations

  • Hiroe Oka
    • 1
  1. 1.Department of Mathematics, Faculty of ScienceKyoto UniversityKyotoJapan

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