The structure of equicontinuous maps

Mai, Jie-Hua

doi:10.1090/S0002-9947-03-03339-7

The structure of equicontinuous maps
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Trans. Amer. Math. Soc. 355 (2003), 4125-4136 Request permission

Abstract:

Let $(X,d)$ be a metric space, and $f:X\rightarrow X$ be a continuous map. In this paper we prove that if $R(f)$ is compact, and $\omega (x,f)\not =\emptyset$ for all $x\in X$, 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 $(h\times g)|S$ of the product map $h\times g$. In addition, we give some still simpler necessary and sufficient conditions of equicontinuous graph maps.

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