Abstract: By introducing the definition of chain ergodicity and its relationship with topological ergodicity, this paper proves that if topological ergodicity is fulfilled, the chain ergodicity will be fulfilled, too, while it’s not true conversely. Further, it is pointed out that the two properties of mapping which meet the demand of pseudoorbit tracing properties are equivalent. In addition, the present paper presents that if the power system squence is fulfilled, its generated converse limit system will be fulfilled, too, and it’s also true conversely and hence develops the corresponding theory of topological ergodicity.

Key words: chain ergodicity, topological ergodicity, converse limit space