Related papers: Iteration of meromorphic functions
The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…
We construct an example of an iterated function system on the line, consisting of linear fractional transformations, such that two of the maps share a fixed points, but the dimension of the attractor equals the conformal dimension, so that…
We show that any uniformly escaping and wandering dynamics of a holomorphic function on a compact subset of the plane can be realised by a transcendental meromorphic function on $\mathbb{C}$. More precisely, let $\varphi$ be a holomorphic…
In this article we consider functions $f$ meromorphic in the unit disk. We give an elementary proof for a condition that is sufficient for the univalence of such functions. This condition simplifies and generalizes known conditions. We…
Let ${\mathbb F}_q$ be a finite field of characteristic two and ${\mathbb F}_q(X_1,...,X_n)$ a rational function field. We use matrix methods to obtain explicit transcendental bases of the invariant subfields of orthogonal groups and…
Noncommutative rational functions appeared in many contexts in system theory and control, from the theory of finite automata and formal languages to robust control and LMIs. We survey the construction of noncommutative rational functions,…
In a previous paper [1] it was discussed the viability of functional analysis using as a basis a couple of generic functions, and hence vectorial decomposition. Here we complete the paradigm exploiting one of the analysis methodologies…
The article is devoted to one infinite parametric class of continuous functions with complicated local structure. In the article differential, integral, self-affine and other properties of functions, that their argument is represented by…
We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…
This paper discusses iterated monodromy groups for transcendental functions. We show that for every post-singularly finite entire transcendental function, the iterated monodromy action can be described by bounded activity automata of a…
The finite families of biorthogonal rational functions and orthogonal polynomials of Hahn type are interpreted algebraically in a unified way by considering the three-generated meta Hahn algebra and its finite-dimensional representations.…
In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential operations is closed. On basis of these works, we…
This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…
This paper introduces Farey Recursive Functions and investigates their basic properties. Farey Recursive Functions are a special type of recursive function from the rationals to a commutative ring. The recursion of these functions is…
If the preimage of a four-point set under a meromorphic function belongs to the real line, then the image of the real line is contained in a circle in the Riemann sphere. We include an application of this result to holomorphic dynamics: if…
In this paper, we obtain the meromorphic continuation of a q-analogue of multiple zeta function using an elementary formula called translation formula. We then obtain the matrix representation of the translation formula and using it, we…
Adopting the approach of [7] we study rational function carrying invariant line fields on the Julia set. In particular, we show that under certain weak conditions all possible measurable invariant line fields of a rational function on its…
The main purpose of this paper is to derive some subordination and superordination results involving certain of integral operator for meromorphic univalent functions in the punctured open unit disk. Several sandwich-type results are also…
We present a one-parameter family $F_\lambda$ of transcendental entire functions with zeros, whose Newton's method yields wandering domains, coexisting with the basins of the roots of $F_\lambda$. Wandering domains for Newton maps of…