Iteration of meromorphic functions
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In this paper, the authors describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions, and some aspects where the transcendental case is analogous to the rational case are treated rather briefly here.Abstract:
This paper attempts to describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions. The reader is not expected to be familiar with the iteration theory of rational functions. On the other hand, some aspects where the transcendental case is analogous to the rational case are treated rather briefly here. For example, we introduce the different types of components of the Fatou set that occur in the iteration of rational functions but omit a detailed description of these types. Instead, we concentrate on the types of components that are special to transcendental functions (Baker domains and wandering domains).read more
Citations
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Meromorphic Functions in the Class S and the Zeros of the Second Derivative
TL;DR: In this article, it was shown that the Gol-dberg conjecture holds for a function in S of finite order, at least on a set of logarithmic density 1.
Journal ArticleDOI
Hausdorff Dimension of Escaping Sets of Nevanlinna Functions
TL;DR: In this paper, the exact values of Hausdorff dimensions of escaping sets of meromorphic functions with polynomial Schwarzian derivatives were derived from the relation between these functions and the second order differential equations in the complex plane.
Journal ArticleDOI
Real analyticity of Jacobian of invariant measures for hyperbolic meromorphic functions
TL;DR: In this paper, it was shown that for a hyperbolic meromorphic function f having a rapid derivative growth, if HD (J(f))>1, the Jacobian of a probability invariant measure μ ϕ on J(f), equivalent to a conformal measure m ϕ, has a real analytic extension on a neighbourhood of J ∖ f −1 (∞) in ℂ.
Journal ArticleDOI
A fundamental dichotomy for Julia sets of a family of elliptic functions
TL;DR: In this paper, the authors investigated topological properties of Julia sets of iterated elliptic functions of the form g = 1/℘, where ℘ is the Weierstrass elliptic function, on triangular lattices.
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Absorbing sets and Baker domains for holomorphic maps
TL;DR: In this article, the authors consider holomorphic maps with parabolic I type for a hyperbolic domain $U$ in the complex plane, such that the iterates of the map converges to a boundary point of the domain.
References
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TL;DR: A can is a can made of a steel sheet the surface of which is coated with a three-layered chromium coating, consisting of a metallic chromium coated, a crystalline chromium oxide coating and a non-crystalline hydrated chromiumoxide coating in this order.