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
The M-set of λ exp(z)/z has infinite area
Guoping Zhan,Liangwen Liao +1 more
TL;DR: In this paper, it was shown that the M-set of λexp(z)/z has infinite area and the Hausdorff dimension of the Mset is 2.
Journal ArticleDOI
The second derivative of a meromorphic function
TL;DR: In this article, the authors strengthen a previous estimate for the frequency of distinct poles of a meromorphic of finite order in the plane, and show that the conjecture is true if either $f$ has order less than $1+\varepsilon, for some positive absolute constant, or $f^{(m)}$, for some 0, m lt k, has few zeros away from the real axis.
Posted Content
Results on escaping set of an entire function and its composition
Ramanpreet Kaur,Dinesh Kumar +1 more
TL;DR: In this article, the authors provided families of transcendental entire functions for which Eremenko's conjecture holds and investigated the dynamical properties of the mapping $f(z)=z+1+e^{-z}.
Journal ArticleDOI
Fatou’s Associates
TL;DR: In this article, it was shown that when the singular values of f in V lie away from the boundary, there is a strong relationship between singularities of g and accesses to infinity in U. In the case of U is a forward-invariant Fatou component of f, this leads to a very significant generalisation of earlier results on the number of singularities.
References
More filters
Journal ArticleDOI
Simple mathematical models with very complicated dynamics
Robert M. May,Robert M. May +1 more
TL;DR: This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.
Book
An introduction to chaotic dynamical systems
TL;DR: In this article, the quadratic family has been used to define hyperbolicity in linear algebra and advanced calculus, including the Julia set and the Mandelbrot set.
Book
Dynamics and Bifurcations
Jack K. Hale,Hüseyin Koçak +1 more
TL;DR: In this paper, the authors present ideas and examples about the geometry of dynamics and bifurcations of ordinary differential equations, and demonstrate that the basic notion of stability and stability of vector fields can be easily explained for scalar autonomous equations.
Book
The Beauty of Fractals
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.