Related papers: Entire functions for which the escaping set is a s…

Let f be a real entire function whose set S(f) of singular values is real and bounded. We show that, if f satisfies a certain function-theoretic condition (the "sector condition"), then $f$ has no wandering domains. Our result includes all…

Approximation theory of entire functions has been used to demonstrate the construction of a map on $\mathbb{C}\times\mathbb{R}$ having wandering domains. We also present suitable modification to this construction that helps in obtaining…

In this paper, we study the dynamics of commuting transcendental entire functions $f$ and $g$, where $g$ is of the form $af^p + b$ with $a,b \in \C$, $p \in \N$, and $a \neq 0,1$. We establish that the escaping sets, filled Julia sets, and…

We consider the dynamics associated with an arbitrary semigroup of transcendental entire functions. Fatou-Julia theory is used to investigate the dynamics of these semigroups. Several results of the dynamics associated with iteration of a…

We consider a class of functions, denoted by K in this paper, which are meromorphic outside a compact and countable set B(f), investigated by A. Bolsch in his thesis in 1997. The set B(f) is the closure of isolated essential singularities.…

Let $g$ and $h$ be transcendental entire functions and let $f$ be a continuous map of the complex plane into itself with $f\circ g=h\circ f.$ Then $g$ and $h$ are said to be semiconjugated by $f$ and $f$ is called a semiconjugacy. We…

Let $f$ and $g$ be two quasiregular maps in $\mathbb{R}^d$ that are of transcendental type and also satisfy $f\circ g =g \circ f$. We show that if the fast escaping sets of those functions are contained in their respective Julia sets then…

A hyperbolic transcendental entire function with connected Fatou set is said to be "of disjoint type". It is known that a disjoint-type function provides a model for the dynamics near infinity of all maps in the same parameter space; hence…

The Fatou-Julia iteration theory of rational functions has been extended to quasiregular mappings in higher dimension by various authors. The purpose of this paper is an analogous extension of the iteration theory of transcendental entire…

Given an entire transcendental function f with a non-completely invariant Baker domain, we define a Baker lamination on geodesics to study the divergence and convergence of a pinching process of curves in U. If the boundary of some curve in…

Providing the neurobiological basis of information processing in higher animals, spiking neural networks must be able to learn a variety of complicated computations, including the generation of appropriate, possibly delayed reactions to…

We consider transcendental entire functions of finite order for which the zeros and $1$-points are in disjoint sectors. Under suitable hypotheses on the sizes of these sectors we show that such functions must have a specific form, or that…

We consider the iteration of quasiregular maps of transcendental type from $\mathbb{R}^d$ to $\mathbb{R}^d$. In particular we study quasi-Fatou components, which are defined as the connected components of the complement of the Julia set.…

We study the different rates of escape of points under iteration by holomorphic self-maps of $\mathbb C^*=\mathbb C\setminus\{ 0\}$ for which both 0 and $\infty$ are essential singularities. Using annular covering lemmas we construct…

We study topological properties of the escaping endpoints and fast escaping endpoints of the Julia set of complex exponential $\exp(z)+a$ when $a\in (-\infty,-1)$. We show neither space is homeomorphic to the whole set of endpoints. This…

A generalized family of transcendental (non-polynomial entire) functions is constructed, where the Hausdorff dimension and the packing dimension of the Julia sets are equal to one. Further, there exist multiply connected wandering domains,…

While the dynamics of transcendental entire functions in periodic Fatou components and in multiply connected wandering domains are well understood, the dynamics in simply connected wandering domains have so far eluded classification. We…

We introduce a new technique that allows us to make progress on two long standing conjectures in transcendental dynamics: Baker's conjecture that a transcendental entire function of order less than 1/2 has no unbounded Fatou components, and…

Let $M$ be the class of all transcendental meromorphic functions $f: \mathbb{C} \to \mathbb{C} \bigcup\{\infty\}$ with at least two poles or one pole that is not an omitted value, and $M_o =\{f \in M:f{has at least one omitted value}\}$.…

Motivated by applications for set containment problems, we consider the following fundamental problem: can we design set-to-vector functions so that the natural partial order on sets is preserved, namely $S\subseteq T \text{ if and only if…