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Some pinching deformations of the Fatou function

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Domínguez P., Sienra G.

Fundamenta Mathematicae

2015

tom 228

nr 1

1-15

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 $F_{p/q}(z) = z + e^{-z} + 2πip/q$, 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 process into doubly parabolic Baker domains.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Domínguez P.

1 Sienra G.

1 2015

Wyniki wyszukiwania

Some pinching deformations of the Fatou function