Peherstorfer, Franz Stroh, Christoph
Published in
Computational Methods and Function Theory

For a polynomial P it is well known that its Julia set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\cal J_P}$\end{document} is connected if and only if the orbits o...

Bergweiler, Walter
Published in
Computational Methods and Function Theory

Let U be a Baker domain of a transcendental entire function f. Denote by λU the hyperbolic metric in U and, for w ∈ U and n ∈ ℕ, define ρn(w) = λ U(fn+1}(w),fn(w)) and ρ(w) = limn→∞ρn(w). Here fn denotes the n-th iterate of f. It is shown that if the set of singularities of f− 1 that are contained in U is bounded, then \documentclass[12pt]{minimal}...

Cao, Chun Lei Wang, Yue Fei
Published in
Acta Mathematica Sinica

We shall show that for certain holomorphic maps, all Fatou components are simply connected. We also discuss the relation between wandering domains and singularities for certain meromorphic maps.

Gumenuk, Pavel
Published in
Computational Methods and Function Theory

Let f be a meromorphic function, and z0 ∈ ℂ its attracting fixed point with multiplier λ ≠ 0. In this paper we consider the problem of finding a lower estimate for the largest number R(z0,f), such that if the function f is univalent and has no poles in the disk of radius ru centered at z0, then \documentclass[12pt]{minimal} \usepackage{amsmath} \us...

Brück, Rainer Büger, Matthias
Published in
Computational Methods and Function Theory

The main purpose of the Fatou-Julia theory is to study the global behaviour of the sequence (fn) of iterates of a rational function f. In this survey article we consider generalized iteration which means that the iterated function f may vary from step to step. More precisely, let (fn) be a sequence of rational functions, and let \documentclass[12pt...

Ding-guo, Zhang Jian-qiang, Xiao
Published in
Applied Mathematics and Mechanics

The dynamics of a coupled rigid-flexible rocket launcher is reported. The coupled rigid-flexible rocket launcher is divided into two subsystems, one is a system of rigid bodies, the other a flexible launch tube which can undergo large overall motions spatially. First, the mathematical models for these two subsystems were established respectively. T...

Dinh, Tien Cuong Dujardin, Romain Sibony, Nessim
Published in
Mathematische Annalen

We construct the Green current for a random iteration of horizontal-like mappings in . This is applied to the study of a polynomial map with the following properties: i. infinity is f-attracting; ii.f contracts the line at infinity to a point not in the indeterminacy set. We study for such mappings the escape rates near infinity, i.e. the set of po...

Singh, A. P. Sharma, R.
Published in
Analysis in Theory and Applications

Let f be an entire function. A point zo is called a critical point of f if f′(zo)=0, and f(zo) is called a critical value (or an algebraic singularity) of f. Next aε is said to be an asymptotic value (or a transcendental singularity) of f if there exists a curve λ:[0,1]→ℂ such that\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasys...

Zhang, Ding-guo Zhou, Sheng-feng
Published in
Applied Mathematics and Mechanics

The dynamic modeling and simulation of an N-flexible-link and N-flexible-joint robot is reported. Each flexible joint is modeled as a linearly elastic torsional spring and the approach of assumed modes is adopted to describe the deformation of the flexible-link. The complete governing equations of motion of the flexible-link-joint robots are derive...

Ishizaki, K. Yanagihara, N.
Published in
Archiv der Mathematik

Let R(w) be a non-inear rational function and s be a complex constant with | s | > 1. It is showed that for any solution f (z) of the Schröder equation f (sz) = R(f (z)), Julia directions of f (z) are also Borel directions of f (z).