Related papers: Bounded Fatou and Julia components of meromorphic …

Given commuting functions f,g, with at most a countable compact set of essential singularities, recent results for entire functions are extended to prove that Julia sets match, J(f)=J(g), in a particular case in the class K. With this…

The subject of this paper is the bounded level curves of a meromorphic function $f$ with domain $G$ such that each component of $\partial{G}$ consists of a level curve of $f$. (A primary example of such a function being a ratio of finite…

We prove a version of the Fatou theorem for bounded functions with bounded d_J-bar diferential on wedge-type domains in an almost complex manifold.

Let $[a,b]\subset\mathbb{R}$ be a non empty and non singleton closed interval and $P=\{a=x_0<\cdots<x_n=b\}$ is a partition of it. Then $f:I\to\mathbb{R}$ is said to be a function of $r$-bounded variation, if the expression…

The goal of this paper is to study some basic properties of the Fatou and Julia sets for a family of holomorphic endomorphisms of $\mathbb{C}^k,\; k \ge 2$. We are particularly interested in studying these sets for semigroups generated by…

We develop a general technique for realising full closed subsets of the complex plane as wandering sets of entire functions. Using this construction, we solve a number of open problems. (1) We construct a counterexample to Eremenko's…

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…

We study the behaviour of a transcendental entire map $ f\colon \mathbb{C}\to\mathbb{C} $ on an unbounded invariant Fatou component $ U $, assuming that infinity is accessible from $ U $. It is well-known that $ U $ is simply connected.…

The ergodic theory and geometry of the Julia set of meromorphic functions on the complex plane with polynomial Schwarzian derivative is investigated under the condition that the forward trajectory of asymptotic values in the Julia set is…

In the main part of the paper, on the basis of contour integration of complex meromorphic functions whose singularities lie onto an integration contour, in the first step, a concept of improper integrals absolute existence of meromorphic…

In this paper, we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.

We investigate to what extent Fatou set, Julia set and escaping set of transcendental semigroup is respectively equal to the Fatou set, Julia set and escaping set of its subsemigroup. We define partial fundamental set and fundamental set of…

We show that for each $d\in (0,2]$ there exists a meromorphic function $f$ such that the inverse function of $f$ has three singularities and the Julia set of $f$ has Hausdorff dimension $d$.

It is known that local zeta functions associated with real analytic functions can be analytically continued as meromorphic functions to the whole complex plane. But, in the case of general ($C^{\infty}$) smooth functions, the meromorphic…

We study the internal dynamics of multiply connected wandering domains of meromorphic functions. We do so by considering the sequence of injectivity radii along the orbit of a base point, together with the hyperbolic distortions along the…

We investigate the meromorphic quasi-modular forms and their $L$-functions. We study the space of meromorphic quasi-modular forms. Then we define their $L$-functions by using the technique of regularized integral. Moreover, we give an…

A result is proved concerning meromorphic functions of finite order in the plane such that all but finitely many zeros of the second derivative are zeros of the first derivative.

We construct the first examples of rational functions defined over a non-archimedean field with certain dynamical properties. In particular, we find such functions whose Julia sets, in the Berkovich projective line, are connected but not…

If M is a Drinfeld module over a local function field L, we may view M as a dynamical system, and consider its filled Julia set J. If J^0 is the connected component of the identity, relative to the Berkovich topology, we give a…

We define iterated monodromy groups of more general structures than partial self-covering. This generalization makes it possible to define a natural notion of a combinatorial model of an expanding dynamical system. We prove that a naturally…