Geodesic
On quasi-nested wandering domains
Filomat, Tome 36 (2022) no. 8, p. 2687

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DOI

In this paper, the nature of the singularity of a meromorphic functions of the form f (z) = 1 h(z) + a for a ∈ C and h is an entire function having a Baker wandering domain, lying over the Baker omitted value is discussed. Various dynamical issues relating to the singular values of f have been studied. Also following are shown in this paper. If a be the Baker omitted value of f then f has a Quasi-nested wandering domain U if and only if there exists {n k } k>0 such that each U n k surrounds a and U n k → a as k → ∞. If f is a function having Quasi-nested wandering domain then all the Fatou components of f are bounded. In particular, f has no Baker domain. Also existence of Quasi-nested wandering domain ensures that the Julia component containing ∞ i.e., J ∞ is a singleton buried component. At the end of the paper a result about the non existence of Quasi-nested wandering domain is given.
DOI : 10.2298/FIL2208687C
Classification : 37F10, 30D05, 37F50
Keywords: omitted values, Baker wandering domains, transcendental meromorphic functions 
Gorac; and Chakraborty; Sanjib Kumar Datta. On quasi-nested wandering domains. Filomat, Tome 36 (2022) no. 8, p. 2687 . doi: 10.2298/FIL2208687C
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