Analysis of Complex Dynamics

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The head investigator, M. Taniguchi introduced a new kind of combinatorial model for the covering structure of an entire function, which is called "a configuration tree". This concept is the counterpart of that of the Cayley graph of a Kleinian group in the context of the Sullivan's dictionary.This new model enabled us to find a very important class of entire functions, which is called the class of structurally finite entire functions. We also discovered that every element of this class has the very explicit representation as a primitive function of a decorated exponential function. As a consequence, we also proved that the Julia set of every structurally finite entire function has the Hausdorff dimension two.Furthermore, very recently we proved the Bell conjecture on explicit representation of multi-connected planar domains affirmatively by using the Hurwitz space, which is a kind of the representation space of holomorphic branched covering structures.