Fields associated with autonomous dynamical systems (Q2733976)

An equivalence relation is defined on the set of \(2\)-forms of rank \(2m\) on \({\mathbb R}\times V\) (where \(V\) is a \(2m\)-dimensional manifold) and it is shown that each equivalence class contains locally a closed \(2\)-form. This result is applied to the field theory associated to the closed \(2\)-form which is characteristic for a certain spray on \({\mathbb R}\times TM\), where \(M\) is a Riemannian manifold.