Sentence:  The iteration of <WSD>holomorphic</WSD> maps of one variable is one of the most lively fields of current mathematical research. Since its beginning in the twenties of this century, the theory of <WSD>holomorphic</WSD> endomorphisms of the Riemann sphere (= rational functions) has become well developed. 
Meaning of the word marked with <WSD> tags:  Complex-differentiable on an open set around every point in its domain.