2 research outputs found
Variational principles for involutive systems of vector fields
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector
field can be characterized by means of a variational principle based on a
one-form. We discuss how a vector field on a manifold can also be characterized
in a similar way by means of an higher order variational principle, and how
this extends to involutive systems of vector fields.Comment: 31 pages. To appear in International Journal of Geometric Methods in
Modern Physics (IJGMMP
Nonlocal aspects of -symmetries and ODEs reduction
A reduction method of ODEs not possessing Lie point symmetries makes use of
the so called -symmetries (C. Muriel and J. L. Romero, \emph{IMA J.
Appl. Math.} \textbf{66}, 111-125, 2001). The notion of covering for an ODE
is used here to recover -symmetries of as
nonlocal symmetries. In this framework, by embedding into a
suitable system determined by the function ,
any -symmetry of can be recovered by a local symmetry of
. As a consequence, the reduction method of Muriel and
Romero follows from the standard method of reduction by differential invariants
applied to .Comment: 13 page