Iteration of meromorphic functions
Reads0
Chats0
TLDR
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
More filters
Journal ArticleDOI
On the singularities of the inverse to a meromorphic function of finite order
TL;DR: In this paper, it was shown that if f is a transcendental meromorphic function, then f with n = 1 takes every finite non-zero value infinitely often, which is a conjecture of Hayman.
Book ChapterDOI
Complex dynamics in higher dimensions
John Erik Fornæss,Nessim Sibony +1 more
TL;DR: The field of complex dynamics in higher dimensions was initiated in the 1920s by Fa-tou as discussed by the authors, who was motivated by studies in Newton's method, celestial mechanics and functional equations.
Book
Value Distribution of Meromorphic Functions
TL;DR: A survey of results after 1970 can be found in this paper, where the authors present a survey of meromorphic functions of finite-order functions with respect to Riemann surfaces.
Journal ArticleDOI
Graphic and numerical comparison between iterative methods
TL;DR: A simplified version of the Newton-Raphson method was proposed by Raphson in 1690 as mentioned in this paper, which is also known as the Newman-Rodriguez method.
Journal ArticleDOI
On semiconjugation of entire functions
Walter Bergweiler,Aimo Hinkkanen +1 more
TL;DR: In this paper, it was shown that if f satisfies a certain condition, which holds, in particular, if f has no wandering domains, then g−1(J(h))=J(f).
References
More filters
Journal ArticleDOI
Some entire functions with fixpoints of every order
TL;DR: For p = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 30] the natural iterate f D (z ) of f (z) is defined by as mentioned in this paper.
Journal ArticleDOI
Selective solutions to transcendental equations
TL;DR: In this article, a combination of global iterative methods, based on the Fatou-Julia theory, and local methods to find selected roots of elementary transcendental equations, z = F ( z, c ), z and c complex, that occur in complex Sturm-Liouville eigenvalue problems, in dielectric spectroscopy and in orbit determination, is presented.