The structure of equicontinuous maps
The structure of equicontinuous maps
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DOI：
10.1090/s0002-9947-03-03339-7
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发表时间：
2003-06
影响因子：
1.3
通讯作者：
J. Mai
中科院分区：
文献类型：
--
作者：
J. Mai
设（X，d）是度量空间，f：X → X是连续映射.本文证明了：如果R（f）是紧的，且对所有x ∈ X，w（x，f）<$= 0，则f是等度连续的当且仅当存在点态递归等距同胚h和点态收敛于不动点v 0的非扩张映射g，使得f一致共轭于子系统（hxg）|S的产品地图h x g。此外，我们还给出了等度连续图映射的一些更简单的充要条件。
Let (X, d) be a metric space, and f : X → X be a continuous map. In this paper we prove that if R(f) is compact, and w(x, f) ¬= O for all x ∈ X, then f is equicontinuous if and only if there exist a pointwise recurrent isometric homeomorphism h and a non-expanding map g that is pointwise convergent to a fixed point v 0 such that f is uniformly conjugate to a subsystem (h x g)|S of the product map h x g. In addition, we give some still simpler necessary and sufficient conditions of equicontinuous graph maps.