Fixed Point Attractors of Dynamical Systems

In this paper, after studying some properties of attracting fixed points, we focus on the conditions on which a fixed point becomes an attractor. And the results are as follows: (1) the fixed point of a system is an attractor when f is a contraction map of a locally compact metric space or an ultimate contraction map of a compact metric space; (2) with respect to one kind of weakly contraction map of a compact metric space, a necessary and sufficient condition of an attracting fixed point is provided.