The structure of equicontinuous maps

Source abstract

Let ( X , d ) (X,d) be a metric space, and f : X → X f:X\rightarrow X be a continuous map. In this paper we prove that if R ( f ) R(f) is compact, and ω ( x , f ) ≠ ∅ \omega (x,f)\not =\emptyset for all x ∈ X x\in X , then f f is equicontinuous if and only if there exist a pointwise recurrent isometric homeomorphism h h and a non-expanding map g g that is pointwise convergent to a fixed point v 0 v_{0} such that f f is uniformly conjugate to a subsystem ( h × g ) | S (h\times g)|S of the product map h × g h\times g . In addition, we give some still simpler necessary and sufficient conditions of equicontinuous graph maps.