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Adjoint symmetries for time-dependent second-order equations. (English) Zbl 0713.58018

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

MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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