拓扑遍历映射的一些性质

Some Remarks on Topologically Ergodic Maps

本文研究拓扑遍历映射.指出对于由不可约方阵所决定的符号空间有限型子转移而言,或紧致交换群的仿射变换及线段上连续自映射而言,拓扑遍历与拓扑可迁这两个概念是一致的.同时还通过例子,指出拓扑遍历是不同于拓扑可迁与拓扑混合的概念.

This paper deals with topologically ergodic maps. In terms of subshifts of finite type determined by an irreducible matrix, affine maps of compacted connected metric abelian group and by continuous maps of closed interval, the two concepts of topologically ergodic map and topologically transitive map are identical. Furthermore, examples show that the topologically ergodic map differs from the topologically mixing map and the topologically transitive map.