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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Dimensions of Julia sets of hyperbolic entire functions
TL;DR: In this article, it was shown that there is a family of hyperbolic transcendental entire functions with infinitely many poles for which the Hausdorff, packing and box dimensions of the Julia set of a rational function are equal.
Posted Content
Meromorphic functions of one complex variable. A survey
TL;DR: Goldberg and Ostrovskii as discussed by the authors survey the results obtained on the topics of the book after 1970 and present an appendix to the English translation of this book by A A Goldberg and I V Ostrovkii, Distribution of values of meromorphic functions.
Journal ArticleDOI
Newton's method and Baker domains
TL;DR: In this paper, it was shown that there exists an entire function f without zeros for which the associated Newton function N(z)=z-f(z)/f'(z) is a transcendental meromorphic function without Baker domains.
Journal ArticleDOI
Iteration of the Translated Tangent
TL;DR: In this article, the iteration of the map on the complex plane is investigated for each complex number and it is shown that its Fatou set always contains a completely invariant component and the Julia set is either totally disconnected or connected.
Journal ArticleDOI
On permutable meromorphic functions
J. W. Osborne,David J. Sixsmith +1 more
TL;DR: In this article, the class of functions meromorphic outside a countable closed set of essential singularities is studied, and it is shown that the set of functions in this class that permute with itself and with the identity map is countably infinite.
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