Abstract
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:
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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.
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2.
Coordinate transformations are a good computational tool.
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© 1985 Springer Science+Business Media New York
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Sanders, J.A., Verhulst, F. (1985). Normal Forms. In: Averaging Methods in Nonlinear Dynamical Systems. Applied Mathematical Sciences, vol 59. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4575-7_6
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DOI: https://doi.org/10.1007/978-1-4757-4575-7_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96229-0
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