摘要：A method for determination and two methods for approximation of the domain of attraction D a (0) of the asymptotically stable zero steady state of an autonomous, ℝ-analytical, discrete dynamical system are presented. The method of determination is based on the construction of a Lyapunov function V, whose domain of analyticity is D a (0). The first method of approximation uses a sequence of Lyapunov functions V p , which converge to the Lyapunov function V on D a (0). Each V p defines an estimate N p of D a (0). For any x ∈ D a (0), there exists an estimate which contains x. The second method of approximation uses a ball B(R) ⊂ D a (0) which generates the sequence of estimates M p = f-p(B(R)). For any x ∈ D a (0), there exists an estimate which contains x. The cases ∂0f <1 and ρ(∂0f) < 1 ≤ ∂0f are treated separately because significant differences occur.
关键词：Differential Equation ; Steady State ; Dynamical System ; Partial Differential Equation ; Ordinary Differential Equation
