拓扑遍历与拓扑双重遍历

杨润生

数学学报 ›› 2003, Vol. 46 ›› Issue (3) : 555-560.

数学学报 ›› 2003, Vol. 46 ›› Issue (3) : 555-560. DOI: 10.12386/A2003sxxb0077
论文

拓扑遍历与拓扑双重遍历

    杨润生
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Topological Ergodicity and Topological Double Ergodicity

    Run Sheng YANG
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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.

Abstract

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

引用本文

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杨润生. 拓扑遍历与拓扑双重遍历. 数学学报, 2003, 46(3): 555-560 https://doi.org/10.12386/A2003sxxb0077
Run Sheng YANG. Topological Ergodicity and Topological Double Ergodicity. Acta Mathematica Sinica, Chinese Series, 2003, 46(3): 555-560 https://doi.org/10.12386/A2003sxxb0077

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