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Some pinching deformations of the Fatou function

Patricia Domínguez, Guillermo Sienra (2015)

Fundamenta Mathematicae

We are interested in deformations of Baker domains by a pinching process in curves. In this paper we deform the Fatou function F ( z ) = z + 1 + e - z , depending on the curves selected, to any map of the form F p / q ( z ) = z + e - z + 2 π i p / q , p/q a rational number. This process deforms a function with a doubly parabolic Baker domain into a function with an infinite number of doubly parabolic periodic Baker domains if p = 0, otherwise to a function with wandering domains. Finally, we show that certain attracting domains can be deformed by a pinching...

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