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Escaping Fatou components of transcendental self-maps of the punctured plane by MARTÃ-PETE, DAVID is a Mathematics article available to read on EtoBox.
What is Escaping Fatou components of transcendental self-maps of the punctured plane about?
Abstract We study the iteration of transcendental self-maps of $\mathcal{C}^*:\=\mathcal{C}\{0}$, that is, holomorphic functions $\fnof:\mathcal{C}^*:\rarr\mathcal{C}^*$ for which both zero and infinity are essential singularities. We use approximation theory to construct functions in this class with escaping Fatou components, both wandering domains and Baker domains, that accumulate to $\{0},\infin$ in any possible way under iteration. We also give the first explicit examples of transcendental self-maps of $\mathcal{C}^*$ with Baker domains and with wandering domains. In doing so, we developed a sufficient condition for a function to have a simply connected escaping wandering domain. Finally, we remark that our results also provide new examples of entire functions with escaping Fatou components.
Who reads Escaping Fatou components of transcendental self-maps of the punctured plane?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- MARTÃ-PETE, DAVID
- Publisher
- Cambridge University Press; Cambridge University Press (CUP) (ISSN 0305-0041)
- Published
- 2019
- Language
- EN
- Field
- Mathematics (Physical Sciences)