Stability investigation of almost periodic discrete system by direct Lyapunov method and limiting equations technique

The construction of topological dynamic of almost periodic discrete system is elaborated as well as the invariance property of positive limit set of it's solution is established. On the basis of synthesis of limiting equations technique and Lyapunov functions method a theorem on localization of positive limit set and several theorems on asymptotic and partial asymptotic stability are proven. The demands on Lyapunov function are relaxed so it admissible to use nonnegative functions with nonpositive first difference.