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Submersive second order ordinary differential equations

Published online by Cambridge University Press:  24 October 2008

Marek Kossowski  and
Gerard Thompson
Marek Kossowski
Affiliation:
Department of Mathematics, University of South Carolina, Columbia, SC 29208, U.S.A.
Gerard Thompson
Affiliation:
Department of Mathematics, University of Toledo, Toledo, OH 43606, U.S.A.
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Extract

The objectives of this paper are to define and to characterize submersive second order ordinary differential equations (ODE) and to examine several situations in which such ODE occur. This definition and characterization is in terms of tangent bundle geometry as developed in [4, 6, 7, 10, 11, 14]. From this viewpoint second order ODE are identified with a special vector field on the tangent bundle. The ODE are said to be submersive when this vector field and the canonical vertical endomorphism [14] define a foliation, relative to which the vector field passes to the local quotient.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 207 - 224
Copyright
Copyright © Cambridge Philosophical Society 1991

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