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

Sigurd B. Angenent, Jan Bouwe van den Berg, Robert C. Vandervorst

• 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.