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Contact and non-contact type Hamiltonian systems generated by second-order Lagrangians

Published online by Cambridge University Press:  28 November 2006

S. B. ANGENENT ,
J. B. VAN DEN BERG  and
R. C. A. M. VANDERVORST
S. B. ANGENENT
Affiliation:
Department of Mathematics, University of Winconsin-Madison, Madison, WI 53706-1388, USA (e-mail: angenent@math.wisc.edu)
J. B. VAN DEN BERG
Affiliation:
Mathematics Department, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
R. C. A. M. VANDERVORST
Affiliation:
Mathematics Department, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands
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Abstract

We show that some very naturally occurring energy manifolds that are induced by second-order Lagrangians $L =L(u,u',u'')$ are not, in general, of contact type in $(\mathbb{R}^4,\omega)$. We also comment on the more general question whether there exist any contact forms on these energy manifolds for which the associated Reeb vector field coincides with the Hamiltonian vector field.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 1 , February 2007 , pp. 23 - 49
Copyright
2006 Cambridge University Press

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