On Transformations into Normal Form

We discuss a certain class of transformations of an ordinary differential equation into normal form near a stationary point. These transformations preserve certain special structures and one can derive from them a universally applicable algorithm to determine a normal form up to any desired degree....

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 180; no. 2; pp. 617 - 632
Main Author Walcher, S.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.12.1993
Elsevier
Subjects
Exact sciences and technology
Mathematical analysis
Mathematics
Ordinary differential equations
Sciences and techniques of general use
Mathematical transformation
Taylor series
Differential equation
Algorithm
Normal form
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Summary:We discuss a certain class of transformations of an ordinary differential equation into normal form near a stationary point. These transformations preserve certain special structures and one can derive from them a universally applicable algorithm to determine a normal form up to any desired degree. The algorithm can be programmed with the help of any computer algebra system. In the same manner, transformations into normal form on an invariant manifold are discussed.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1993.1420