scholarly journals A class of adding machines and Julia sets

2016 ◽  
Vol 36 (11) ◽  
pp. 5951-5970
Author(s):  
Danilo Antonio Caprio
Keyword(s):  
Julia Sets ◽  
Adding Machines

scholarly journals SPECTRUM OF STOCHASTIC ADDING MACHINES AND FIBERED JULIA SETS

2013 ◽  
Vol 13 (03) ◽  
pp. 1250021 ◽  
Author(s):  
ALI MESSAOUDI ◽  
OLIVIER SESTER ◽  
GLAUCO VALLE
Keyword(s):  
Markov Chains ◽  
Julia Sets ◽  
Basic Algorithm ◽  
Analytical Properties ◽  
Transition Operators ◽  
Adding Machines

Consider the basic algorithm to perform the transformation n ↦ n + 1 changing digits of the d-adic expansion of n one by one. We obtain a family of Markov chains on the non-negative integers through successive and independent applications of the algorithm modified by a parametrized stochastic rule that randomly prevents one of the steps in the algorithm to finish. The objects of study in this paper are the spectra of the transition operators of these Markov chains. The spectra of these Markov chains turn out to be fibered Julia sets of fibered polynomials. This enables us to analyze their topological and analytical properties with respect to the underlying parameters of the Markov chains.

scholarly journals Generalized adding machines and Julia sets

2016 ◽  
Vol 354 (11) ◽  
pp. 1096-1100
Author(s):  
Ali Messaoudi ◽  
Glauco Valle
Keyword(s):  
Julia Sets ◽  
Adding Machines

FIXED POINTS-JULIA SETS

2020 ◽  
Vol 9 (9) ◽  
pp. 6759-6763
Author(s):  
G. Subathra ◽  
G. Jayalalitha
Keyword(s):  
Fixed Points ◽  
Julia Sets

Dynamics of a family of orbitally continuous mappings

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3507-3517
Author(s):  
Abhijit Pant ◽  
R.P. Pant ◽  
Kuldeep Prakash
Keyword(s):  
Fixed Points ◽  
Julia Sets ◽  
Real Numbers ◽  
Continuous Mappings ◽  
Non Linear

The aim of the present paper is to study the dynamics of a class of orbitally continuous non-linear mappings defined on the set of real numbers and to apply the results on dynamics of functions to obtain tests of divisibility. We show that this class of mappings contains chaotic mappings. We also draw Julia sets of certain iterations related to multiple lowering mappings and employ the variations in the complexity of Julia sets to illustrate the results on the quotient and remainder. The notion of orbital continuity was introduced by Lj. B. Ciric and is an important tool in establishing existence of fixed points.

scholarly journals Locally connected models for Julia sets

2011 ◽  
Vol 226 (2) ◽  
pp. 1621-1661 ◽  
Author(s):  
Alexander M. Blokh ◽  
Clinton P. Curry ◽  
Lex G. Oversteegen
Keyword(s):  
Julia Sets

Fractal analysis and control of the competition model

2016 ◽  
Vol 09 (03) ◽  
pp. 1650045 ◽  
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.

scholarly journals Quasisymmetric geometry of the Julia sets of McMullen maps

2018 ◽  
Vol 61 (12) ◽  
pp. 2283-2298 ◽  
Author(s):  
Weiyuan Qiu ◽  
Fei Yang ◽  
Yongcheng Yin
Keyword(s):  
Julia Sets
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