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Quasiconformal Surgery in Holomorphic Dynamics by Núria Fagella, Bodil Branner

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8

Cut and paste surgeries with sectors

In this chapter we give three different applications of cut and paste surgeries, including their dependence on parameters. We plough in the dynamical planes and harvest in parameter spaces. In all three cases we start by a polynomial in a limb of the connectedness locus of a one-parameter family, or by a polynomiallike map hybrid equivalent to such one.

In Section 8.2 we show how it is possible, through surgery, to change a certain given map and its phase space in such a way that the new map on its new phase space has an extra critical point. Adding parameters to the construction, we obtain homeomorphisms between parameter spaces of different families. The first construction of this kind occurred in [BD ...

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