Sarlet, W.; Prince, G. E.; Crampin, M. Adjoint symmetries for time-dependent second-order equations. (English) Zbl 0713.58018 J. Phys. A, Math. Gen. 23, No. 8, 1335-1347 (1990). The notion of adjoint symmetries is the main subject of the paper (for time-dependent second-order equations). These symmetries introduced as a particular type of 1-form, whose leading coefficients satisfy the adjoint equations of the equations determining symmetry vector autonomous theory, have their counterparts in the present framework. Of particular interest is a result establishing that Lagrangian systems seem to be the only ones for which there is a natural duality between symmetries and adjoint symmetries. It is important for generalizing Noether’s theorem. The correspondence between pseudo-symmetries and such adjoint symmetries is linking the two different paths for generalizing Noether’s theorem. Reviewer: P.Khmelevskaja Cited in 18 Documents MSC: 37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems Keywords:adjoint symmetries; time-dependent second-order equations; Lagrangian systems; Noether’s theorem PDFBibTeX XMLCite \textit{W. Sarlet} et al., J. Phys. A, Math. Gen. 23, No. 8, 1335--1347 (1990; Zbl 0713.58018) Full Text: DOI