Let (X,d) be a compact metric space and f a continuous transformation on X. f has the specification if one can always find a single orbit to interpolate between different pieces of orbits, up to a preassigned error. We call the map \mu to h_{\mu}(f) (KolmogorovSinai entropy)the entropy map . Does specification implies that entropy map is upper semicontinuous?
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Expansivity implies that the entropy map is upper semicontinuous. See P. walters book Thm 8.2. I think that if the shadowing orbit in your definition of specification is unique then the map f is expansive. 

