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On multiply-connected Fatou components in iteration of meromorphic functions
2006
Journal of Mathematical Analysis and Applications
Let f : C →Ĉ be a transcendental meromorphic function with at most finitely many poles. We mainly investigated the existence of the Baker wandering domains of f (z) and proved, among others, that if f (z) has a Baker wandering domain U , then for all sufficiently large n, f n (U ) contains a round annulus whose module tends to infinity as n → ∞ and so for some 0 < d < 1, M c (r, a, f ) d m c (r, a, f ), r ∈ G, where G is a set of positive numbers with infinite logarithmic measure. Therefore, we
doi:10.1016/j.jmaa.2005.05.038
fatcat:jaj4wdobgzc7bdtvqcu6afqhr4