Some pinching deformations of the Fatou function

Patricia Domínguez; Guillermo Sienra

Fundamenta Mathematicae, Tome 228 (2015), p. 1-15 / Harvested from The Polish Digital Mathematics Library

Résumé

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 process into doubly parabolic Baker domains.

Publié le : 2015-01-01

Zbl 06366987

EUDML-ID : urn:eudml:doc:283031

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     author = {Patricia Dom\'\i nguez and Guillermo Sienra},
     title = {Some pinching deformations of the Fatou function},
     journal = {Fundamenta Mathematicae},
     volume = {228},
     year = {2015},
     pages = {1-15},
     zbl = {06366987},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-1}
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Patricia Domínguez; Guillermo Sienra. Some pinching deformations of the Fatou function. Fundamenta Mathematicae, Tome 228 (2015) pp. 1-15. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm228-1-1/