相关论文: Iteration of some topologically hyperbolic maps in…

In this article, the dynamics of a one-parameter family of functions $f_{\lambda}(z) = \frac{\sin{z}}{z^2 + \lambda},$ $\lambda>0$, are studied. It shows the existence of parameters $0< \lambda_{1}< \lambda_{2}$ such that bifurcations occur…

An omitted value of a transcendental meromorphic function $f$ is called a Baker omitted value, in short \textit{bov} if there is a disk $D$ centered at the bov such that each component of the boundary of $f^{-1}(D)$ is bounded. Assuming…

Let $f:\mathbb C\to \widehat{\mathbb C}=\mathbb C \cup\{\infty\}$ be a transcendental meromorphic function (possibly without any pole) with a single essential singularity, and that is chosen to be at $\infty$. The set of points…

We study the iteration of transcendental self-maps of $\mathbb{C}^*:=\mathbb{C}\setminus \{0\}$, that is, holomorphic functions $f:\mathbb{C}^*\to\mathbb{C}^*$ for which both zero and infinity are essential singularities. We use…

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…

Dynamics of an one-parameter family of functions $f_\lambda(z)=\lambda + z+\tan z, z \in \mathbb{C}$ and $\lambda \in \mathbb{C}$ with an unbounded set of singular values is investigated in this article. For $|2+\lambda^2|<1$, $\lambda=i$,…

Let $f$ be a rational map with an infinitely-connected fixed parabolic Fatou domain $U$. We prove that there exists a rational map $g$ with a completely invariant parabolic Fatou domain $V$, such that $(f,U)$ and $(g,V)$ are conformally…

We consider the transcendental entire function $ f(z)=z+e^{-z} $, which has a doubly parabolic Baker domain $U$ of degree two, i.e. an invariant stable component for which all iterates converge locally uniformly to infity, and for which the…

We show that an invariant Fatou component of a hyperbolic transcendental entire function is a bounded Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. We use this…

Let $f$ be a transcendental entire function of finite order which has an attracting periodic point $z_0$ of period at least $2$. Suppose that the set of singularities of the inverse of $f$ is finite and contained in the component $U$ of the…

We prove several results concerning the relative position of points in the postsingular set $P(f)$ of a meromorphic map $f$ and the boundary of a Baker domain or the successive iterates of a wandering component. For Baker domains we answer…

For a transcendental entire function f, we study the set of points BU(f) whose iterates under f neither escape to infinity nor are bounded. We give new results on the connectedness properties of this set and show that, if U is a Fatou…

In this paper, we show that there exist transcendental meromorphic functions with a cycle of 2-periodic Fatou components, where one is simply connected while the other is doubly connected. In particular, the doubly connected Fatou component…

We study the dynamical behaviour of points in the boundaries of simply connected invariant Baker domains $U$ of meromorphic maps $f$ with a finite degree on $U$. We prove that if $f|_U$ is of hyperbolic or simply parabolic type, then almost…

We investigate the existence of wandering Fatou components for polynomial skew-products in two complex variables. In 2004 the non-existence of wandering domains near a super-attracting invariant fiber was shown in [8]. In 2014 it was shown…

Let f be a transcendental entire map that is subhyperbolic, i.e., the intersection of the Fatou set F(f) and the postsingular set P(f) is compact and the intersection of the Julia set J(f) and P(f) is finite. Assume that no asymptotic value…

A Baker omitted value, in short \textit{bov} of a transcendental meromorphic function $f$ is an omitted value such that there is a disk $D$ centered at the bov for which each component of the boundary of $f^{-1}(D)$ is bounded. Assuming all…

We first establish any continuum without interiors can be a limit set of iterations of an entire function on an oscillating wandering domain, and hence arise as a component of Julia sets. Recently, Luka Boc Thaler showed that every bounded…

We prove that the meandering set for $f_a(z)=e^z+a$ is homeomorphic to the space of irrational numbers whenever $a$ belongs to the Fatou set of $f_a$. This extends recent results by Vasiliki Evdoridou and Lasse Rempe. It implies that the…

We study the family of singular perturbations of Blaschke products $B_{a,\lambda}(z)=z^3\frac{z-a}{1-\overline{a}z}+\frac{\lambda}{z^2}$. We analyse how the connectivity of the Fatou components varies as we move continuously the parameter…