Surgery in Complex Dynamics

Complex rational maps and entire functions define dynamical systems on the Riemann sphere or on the complex plane, and their behavior is remarkably complex. The sphere or the plane are divided into Fatou set and Julia set, according to whether the orbits are tame or chaotic. One basic question is what kind of dynamics can occur when the maps are restricted to a certain class. Surgery is one of the tools which allows us to answer some of these questions.  By using quasiconformal mappings and the measurable conformal mapping theorem, we are able to modify given analytic maps and create new analytic dynamics.  In the talk, I will explain the basic idea of quasiconformal surgery and some examples of surgery of entire functions.

Mitsuhiro Shishikura

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