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Linearizations of ordinary differential equations by area preserving maps

Published online by Cambridge University Press:  22 January 2016

Tetsuya Ozawa  and
Hajime Sato
Tetsuya Ozawa
Affiliation:
Department of Math. Meijo Univ., Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502, Japan, ozawa@meijo-u.ac.jp
Hajime Sato
Affiliation:
Graduate School of Math. Nagoya Univ., Chikusa-ku, Nagoya 464-8602, Japan, hsato@math.nagoya-u.ac.jp
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Abstract

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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.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 156 , 1999 , pp. 109 - 122
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

References

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