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Summary: Ergod. Th. & Dynam. Sys. (1111), 11, 1
Printed in the United Kingdom c 1111 Cambridge University Press
Contact and noncontact type Hamiltonian
systems generated by second order Lagrangians
S.B. ANGENENT, J.B. VAN DEN BERG and R.C.A.M. VANDERVORST
Department of Mathematics, UW Madison,
Mathematics Department, Vrije Universiteit Amsterdam
(Received Jan 12, 2006)
Abstract. We show that some very naturally occurring energy manifolds that are induced by
second order Lagrangians L = L(u, u
, u
), are in general not of contact type in (R4
, ).
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
Hamiltionian vector field.
1. Introduction
This paper was motivated by the question "are the level sets of the Hamiltonian H : R4
R associated to the variational problem
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