The concept of isodynamism (equivalence) of the influence of parameters on the evolution of a dynamic system is introduced. The method of isodynamism detection is demonstrated for the case of a nonlinear ring interferometer, which is used in atmospheric adaptive optics. The concept of isodynamism allows constructing an algorithm providing for likeness of the evolutions of two systems. This approach, for example, suggests a method for compensation for optical vortex influence on the processes in a nonlinear ring interferometer.