A method of the analysis of strong stability of symplectic matrix is presented. This method is based on spectral dichotomy methods of a matrix with respect to a circle whose new variant has been proposed. Applying the original idea proposed by S. K. Godunov, an algorithm of the analysis of strong stability is proposed. Numerical examples are presented to confirm the theory.

symplectic matrix, spectral dichotomy, spectral projector, spectral portrait, strong stability.