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Quasiconformal Surgery in Holomorphic Dynamics by Núria Fagella, Bodil Branner

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Introduction

The theory of one-dimensional complex dynamical systems, understood as the global study of iteration of holomorphic mappings, has its roots in the early twentieth century with the work of Pierre Fatou and Gaston Julia. Local studies had been successfully attempted earlier, but it was Fatou and Julia’s seminal work, inspired by Paul Montel’s notion of normal families of mappings (then relatively new), that set the basis of what is known today as holomorphic dynamics. Both Fatou and Julia studied extensively the basic partition of the dynamical space into the two disjoint, completely invariant subsets, the Fatou set, which is the open set where tame dynamics occur – the set where Montel’s normality appears – and its complement, the ...

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