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

• Autores: Sigurd B. Angenent, Jan Bouwe van den Berg, Robert C. Vandervorst
• Localización: Ergodic theory and dynamical systems, ISSN 0143-3857, Vol. 27, Nº 1, 2007, págs. 23-49
• Idioma: inglés
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• Resumen

  • 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.