Normal Forms

  • Jan A. Sanders
  • Ferdinand Verhulst
Part of the Applied Mathematical Sciences book series (AMS, volume 59)


In this chapter we shall consider the idea of normal form in the context of averaging. Loosely speaking, a mathematical object, be it a matrix, a function or a vector field, to name but a few, is said to be in normal form if it is ‘reasonably simple’ and is obtained by coordinate transformations:
  1. 1.

    Properties of mathematical objects should not depend on the choice of coordinates, so if one transforms one object onto another by a coordinate transformation, the two are equivalent.

  2. 2.

    Coordinate transformations are a good computational tool.



Vector Field Normal Form Coordinate Transformation Mathematical Object Cotangent Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • Jan A. Sanders
    • 1
  • Ferdinand Verhulst
    • 2
  1. 1.Department of Mathematics and Computer ScienceFree UniversityAmsterdamThe Netherlands
  2. 2.Mathematical InstituteState University of UtrechtUtrechtThe Netherlands

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