Adjoint symmetries of second-order differential equations and generalizations. (English) Zbl 0787.58018

Sarlet, W.

Janyška, Josef (ed.) et al., Differential geometry and its applications. International conference, Brno, Czechoslovakia, 27 Aug. - 2 Sept. 1989. Singapore: World Scientific. 412-421 (1990).

Summary: We briefly recall the concept of adjoint symmetries of a second-order equation field \(\Gamma\) on \(TM\): adjoint symmetries are 1-forms which in a sense are the dual objects of the symmetry vector fields of \(\Gamma\). A first generalization is about time-dependent systems, where we show that all results of the autonomous case remain valid. We next discuss the generalization to higher-order differential equations. Here, the situation is in some respects substantially different, but it appears that the main features of the theory survive the complications.
For the entire collection see [Zbl 0777.00040].

MSC:

37J99	Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37C80	Symmetries, equivariant dynamical systems (MSC2010)
70H03	Lagrange’s equations

Keywords:

ordinary differential equations; higher-order tangent bundles; Lagrangian systems; adjoint symmetries