The groupoid C*-algebra of a rational map
  This paper contains a quite detailed description of the C*-algebra arising from the transformation groupoid of a rational map of degree at least two on the Riemann sphere. The algebra is decomposed stepwise via extensions of familiar C*-algebras whose nature depend on the structure of the Julia set and the stable regions in the Fatou set, as well as on the behaviour of the critical points. 
Klaus Thomsen
math.OA math.DS