ИСТИНА

It is known that the generalized system of relativistic electrodynamics equations can be obtained by the principle of minimal action when solving a variational extremal problem of maximizing a certain special functional. The possibility of using the homotopy (deformation) method for studying the invariance of extremals for the generalized system of equations of relativistic electrodynamics is considered in this paper. This method makes it possible to investigate the stability of extremals of the action functional. An analysis of the Lyapunov’s stability of solutions of this system is carried out by a deformation (homotopy) method for Hamiltonian systems. Keywords: relativistic electrodynamics, variational extremal problem, integro-differential equation, electromagnetic Minkowski potential, one-parameter kind of Hamiltonian systems, deformation method for Hamiltonian systems