Geometric aspects of reduction of order

Authors:
James Sherring and Geoff Prince

Journal:
Trans. Amer. Math. Soc. **334** (1992), 433-453

MSC:
Primary 58F35; Secondary 34A05, 34A26, 58G35

DOI:
https://doi.org/10.1090/S0002-9947-1992-1149125-6

MathSciNet review:
1149125

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Abstract: Using the differential geometry of vectorfields and forms we reinterpret and extend the traditional idea of an integrating factor for a first order differential equation with symmetry. In particular, we provide a simple and manifestly geometric approach to reduction of order via symmetry for ordinary differential equations which largely obviates the necessity for canonical coordinates and the associated quotient manifolds. In so doing, some new results which generalise the class of Lie group actions which can be used to solve ordinary differential equations are developed.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1992-1149125-6

Keywords:
Reduction of order,
symmetry of a differential equation,
symmetry of a Pfaffian system

Article copyright:
© Copyright 1992
American Mathematical Society