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Closed characteristics of second-order Lagrangians

Published online by Cambridge University Press:  12 July 2007

W. D. Kalies  and
R. C. A. M. VanderVorst
W. D. Kalies
Affiliation:
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA
R. C. A. M. VanderVorst
Affiliation:
Department of Mathematics, Vrije Universiteit Amsterdam, de Boelelaan 1081, Amsterdam, The Netherlands
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Abstract

We study the existence of closed characteristics on three-dimensional energy manifolds of second-order Lagrangian systems. These manifolds are always non-compact, connected and not necessarily of contact type. Using the specific geometry of these manifolds, we prove that the number of closed characteristics on a prescribed energy manifold is bounded below by its second Betti number, which is easily computable from the Lagrangian.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 1 , February 2004 , pp. 143 - 158
Copyright
Copyright © Royal Society of Edinburgh 2004

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