Nagoya Mathematical Journal

Linearizations of ordinary differential equations by area preserving maps

Tetsuya Ozawa and Hajime Sato

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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

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

First available in Project Euclid: 27 April 2005

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Zentralblatt MATH identifier

Primary: 34A26: Geometric methods in differential equations


Ozawa, Tetsuya; Sato, Hajime. Linearizations of ordinary differential equations by area preserving maps. Nagoya Math. J. 156 (1999), 109--122.

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