## Nagoya Mathematical Journal

### Linearizations of ordinary differential equations by area preserving maps

#### 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

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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