Discrete conditions of Lyapunov stability

Abstract: We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of hypersurfaces instead of the Lyapunov functions, and conditions on the right part of the differential equation instead of conditions on a Lyapunov function along trajectories of the equation.