On the features of the trajectories of autonomous discrete systems generated by a multiplicity factor of eigenvalues of state matrices

The paper presents research made on deflection of trajectories of discrete systems in the norm of state vector of free motion from the monotone development in the case of multiple real positive eigenvalues of state matrices. It was found that the magnitude of deflection of the trajectories from monotone development increases with the approach of multiple eigenvalue to one and increase in its multiplicity. An analytical expression that was obtained in this work allows to estimate the magnitude of deflection. Results are illustrated by examples of computer modeling.