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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Geometric aspects of reduction of order
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by James Sherring and Geoff Prince PDF
Trans. Amer. Math. Soc. 334 (1992), 433-453 Request permission

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
  • © Copyright 1992 American Mathematical Society
  • 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