Normal Forms

  • Richard H. Rand
  • Dieter Armbruster
Part of the Applied Mathematical Sciences book series (AMS, volume 65)


Like Lindstedt’s method, the method of normal forms is used for obtaining approximate solutions to ordinary differential equations. In contrast to Lindstedt’s method, however, the method of normal forms does not involve expanding the solution in an infinite series. Rather, the idea is to transform the differential equations themselves into a form which is easily solved. The method involves generating a transformation of coordinates (i.e. dependent variables) in the form of an infinite series, and computing the coefficients of the series so that the resulting transformed differential equations are in a normal (i.e., a simple or canonical) form.


Normal Form Hopf Bifurcation High Order Term Infinite Series Previous Transformation 
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Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Richard H. Rand
    • 1
  • Dieter Armbruster
    • 2
  1. 1.Department of Theoretical & Applied MechanicsCornell UniversityIthacaUSA
  2. 2.Institut für Informations-verarbeitungUniversität Tübingen74 Tübingen 1Germany

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