Nagoya Mathematical Journal

Linearizations of ordinary differential equations by area preserving maps

Tetsuya Ozawa and Hajime Sato

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Abstract

We clarify the class of second and third order ordinary differential equations which can be tranformed to the simplest equations $Y''=0$ and $Y'''=0$. The coordinate changes employed to transform the equations are respectively area preserving maps for second order equations and contact form preserving maps for third order equations. A geometric explanation of the results is also given by using connections and associated covariant differentials both on tangent and cotangent spaces.

Article information

Source
Nagoya Math. J., Volume 156 (1999), 109-122.

Dates
First available in Project Euclid: 27 April 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1114631301

Mathematical Reviews number (MathSciNet)
MR1727893

Zentralblatt MATH identifier
0952.34039

Subjects
Primary: 34A26: Geometric methods in differential equations

Citation

Ozawa, Tetsuya; Sato, Hajime. Linearizations of ordinary differential equations by area preserving maps. Nagoya Math. J. 156 (1999), 109--122. https://projecteuclid.org/euclid.nmj/1114631301


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References

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