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Abstract: Let (X,T) be a minimal flow and let x,y in X. An obvious necessary condition for there to be an automorphism f of (X,T) with f(x)=y is that (x,y) be an almost periodic point of the product flow The flow (X,T) is said to be regular if this is always the case. Regular minimal flows are the minimal left ideals of the enveloping semigroup of a flow.
A further necessary condition for the existence of an automorphism is given in terms of the automorphism group of the universal minimal flow, namely that if (m,n) projects to (x,y) and g(m)=n, then g must be in the normalizer of the Ellis group of (X,T). When this always occurs (X,T) is said to be semi regular. Every minimal flow has a semi regular one in the same proximal class.