Related papers: Iterates of Meromorphic Functions on Escaping Fato…
In this paper, we have investigated the sufficient conditions for periodicity of meromorphic functions and obtained two results directly improving the result of \emph{Bhoosnurmath-Kabbur} \cite{Bho & Kab-2013}, \emph{Qi-Dou-Yang} \cite{Qi &…
We investigate the rate of convergence of the iterates of an n-dimensional quasiregular mapping within the basin of attraction of a fixed point of high local index. A key tool is a refinement of a result that gives bounds on the distortion…
The maximum of the modulus of a meromorphic function cannot be restricted from above by the Nevanlinna characteristic of this meromorphic function. But integrals from the logarithm of the module of a meromorphic function allow similar…
Let T be the unit circle, f be an \alpha-Holder continuous function on T, \alpha>1/2, and A be the algebra of continuous function in the closed unit disk \bar D that are holomorphic in D. Then f extends to a meromorphic function in D with…
The dynamics of transcendental functions in the complex plane has received a significant amount of attention. In particular much is known about the description of Fatou components. Besides the types of periodic Fatou components that can…
We relate two conjectures that play a central role in the reported proof of Rota's Conjecture. Let $\mathbb F$ be a finite field. The first conjecture states that: the branch-width of any $\mathbb F$-representable $N$-fragile matroid is…
The interaction between a pair of Bloch fronts forming a traveling domain in a bistable medium is studied. A parameter range beyond the nonequilibrium Ising-Bloch bifurcation is found where traveling domains collapse. Only beyond a second…
Let K be a non-archimedean field with residue field k, and suppose that k is not an algebraic extension of a finite field. We prove two results concerning wandering domains of rational functions f in K(z) and Rivera-Letelier's notion of…
We determine the exact values of Hausdorff dimensions of escaping sets of meromorphic functions with polynomial Schwarzian derivatives. This will follow from the relation between these functions and the second order differential equations…
In order to analyse the way in which the size of the iterates $(f^n(z))$ of a transcendental entire function $f$ can behave, we introduce the concept of the {\it annular itinerary} of a point $z$. This is the sequence of non-negative…
Let $f$ be a transcendental entire function. By a result of Rippon and Stallard, there exist points whose orbit escapes arbitrarily slowly. By using a range of techniques to prove new covering results, we extend their theorem to prove the…
In this paper we introduce an interesting family of relative fractal drums (RFDs in short) at infinity and study their complex dimensions which are defined as the poles of their associated Lapidus (distance) fractal zeta functions…
Highly accurate numerical results for single-particle spectrum and order parameter are obtained for the magnetically ordered Kondo lattice by means of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo…
Let $f\colon X\to X$ be a dominant meromorphic self-map of a compact complex variety $X$ in the Fujiki class $\mathcal{C}$. If the topological degree of $f$ is strictly larger than the other dynamical degrees of $f$, we show that the number…
Motility-induced phase separation (MIPS) is a purely non-equilibrium phenomenon in which self-propelled particles phase separate without any attractive interactions. One surprising feature of MIPS is the emergence of polar, nematic, and…
We study invariant measures for random countable (finite or infinite) conformal iterated function systems (IFS) with arbitrary overlaps. We do not assume any type of separation condition. We prove, under a mild assumption of finite entropy,…
We introduce a family of two-dimensional reflected random walks in the positive quadrant and study their Martin boundary. While the minimal boundary is systematically equal to a union of two points, the full Martin boundary exhibits an…
The stochastic motion of particles in living cells is often spatially inhomogeneous with a higher effective diffusivity in a region close to the cell boundary due to active transport along actin filaments. As a first step to understand the…
Let $f$ be an entire function with the form $f(z)=P(e^z)/e^z$, where $P$ is a polynomial with degree at least $2$ and $P(0)\neq 0$. We prove that the area of the complement of the fast escaping set (hence the Fatou set) of $f$ in a…
Nevanlinna functions are meromorphic functions with a finite number of asymptotic values and no critical values. In [KK2] it was proved that if the orbits of all the asymptotic values accumulate on a compact set on which the function acts…