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

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