Symmetries on a Julia set

EIGENVALUES OF FIBONACCI STOCHASTIC ADDING MACHINE

Stochastics and Dynamics ◽

10.1142/s0219493710002966 ◽

2010 ◽

Vol 10 (02) ◽

pp. 291-313 ◽

Cited By ~ 6

Author(s):

A. MESSAOUDI ◽

D. SMANIA

Keyword(s):

Julia Set ◽

Transition Operator ◽

Complex Numbers ◽

Topological Properties

In this work, we compute the eigenvalues of the transition operator associated to the Fibonacci stochastic adding machine. In particular, we show that the eigenvalues are connected to the set [Formula: see text] of complex numbers z where (z2, z) belongs to the filled Julia set of a particular endomorphism of ℂ2. We also study some topological properties of the set [Formula: see text].

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Dynamics of a Discrete Brusselator Model: Escape to Infinity and Julia Set

Milan Journal of Mathematics ◽

10.1007/s00032-005-0036-y ◽

2005 ◽

Vol 73 (1) ◽

pp. 1-17 ◽

Cited By ~ 12

Author(s):

Hunseok Kang ◽

Yakov Pesin

Keyword(s):

Julia Set ◽

Brusselator Model

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On the Julia set of the perturbed Mandelbrot map

Chaos Solitons & Fractals ◽

10.1016/s0960-0779(99)00101-0 ◽

2000 ◽

Vol 11 (13) ◽

pp. 2067-2073 ◽

Cited By ~ 32

Author(s):

John Argyris ◽

Theodoros E Karakasidis ◽

Ioannis Andreadis

Keyword(s):

Julia Set

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On uniformly perfect boundary of stable domains in iteration of meromorphic functions II

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004101005813 ◽

2002 ◽

Vol 132 (3) ◽

pp. 531-544 ◽

Cited By ~ 8

Author(s):

ZHENG JIAN-HUA

Keyword(s):

Entire Function ◽

Meromorphic Function ◽

Meromorphic Functions ◽

Julia Set ◽

Fatou Set ◽

Deficient Value ◽

Uniformly Perfect ◽

Simply Connected ◽

Stable Domains ◽

Uniform Perfectness

We investigate uniform perfectness of the Julia set of a transcendental meromorphic function with finitely many poles and prove that the Julia set of such a meromorphic function is not uniformly perfect if it has only bounded components. The Julia set of an entire function is uniformly perfect if and only if the Julia set including infinity is connected and every component of the Fatou set is simply connected. Furthermore if an entire function has a finite deficient value in the sense of Nevanlinna, then it has no multiply connected stable domains. Finally, we give some examples of meromorphic functions with uniformly perfect Julia sets.

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Singular perturbations of the unicritical polynomials with two parameters

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2015.114 ◽

2016 ◽

Vol 37 (6) ◽

pp. 1997-2016 ◽

Cited By ~ 1

Author(s):

YINGQING XIAO ◽

FEI YANG

Keyword(s):

Julia Set ◽

Dynamical Behavior ◽

Rational Maps ◽

Topological Properties ◽

Fatou Set ◽

The Family ◽

Image Position ◽

Two Parameters ◽

Unicritical Polynomials

In this paper, we study the dynamics of the family of rational maps with two parameters $$\begin{eqnarray}f_{a,b}(z)=z^{n}+\frac{a^{2}}{z^{n}-b}+\frac{a^{2}}{b},\end{eqnarray}$$ where $n\geq 2$ and $a,b\in \mathbb{C}^{\ast }$. We give a characterization of the topological properties of the Julia set and the Fatou set of $f_{a,b}$ according to the dynamical behavior of the orbits of the free critical points.

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Fractal analysis and control of the competition model

International Journal of Biomathematics ◽

10.1142/s1793524516500455 ◽

2016 ◽

Vol 09 (03) ◽

pp. 1650045 ◽

Cited By ~ 6

Author(s):

Mianmian Zhang ◽

Yongping Zhang

Keyword(s):

Feedback Control ◽

Mathematical Models ◽

Fractal Analysis ◽

Fractal Geometry ◽

Julia Set ◽

Julia Sets ◽

Competition Model ◽

Simulation Results ◽

Population Competition ◽

And Control

Lotka–Volterra population competition model plays an important role in mathematical models. In this paper, Julia set of the competition model is introduced by use of the ideas and methods of Julia set in fractal geometry. Then feedback control is taken on the Julia set of the model. And synchronization of two different Julia sets of the model with different parameters is discussed, which makes one Julia set change to be another. The simulation results show the efficacy of these methods.

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