拓扑遍历与拓扑双重遍历  

Topological Ergodicity and Topological Double Ergodicity

作　　者：杨润生[1] 

机构地区：[1]南京师范大学数学与计算机科学学院,南京210097

出　　处：《数学学报（中文版）》2003年第3期555-560,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10271057);江苏省自然科学基金资助项目(BK2001108)

摘　　要：令X为紧致度量空间,f:X→X为连续映射,U,V为X的任意非空开集,若{n>0|fn(U)∩V≠ )为正上密度集,则称f拓扑遍历.f拓扑双重遍历意味着f×f拓扑遍历.本文在[2]的基础上进一步讨论拓扑遍历与拓扑双重遍历映射的性质.Let X be a compact metric space and f : X →X a continuous onto map. f is called topologically ergodic if for any nonempty open sets U, V of X, {n > O | fn(U)∪ V ≠} is a set of positive upper density. Topological double ergodicity means that f@f is topologically ergodic. In this paper, we shall use the results in [2] to study the properties of topologically ergodic maps and topologically double ergodic maps.

关 键 词：拓扑遍历 拓扑双重遍历 等度连续 处处混沌 

分 类 号：O189.3[理学—数学]