**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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