Result: Research on fractal structure of generalized M-J sets utilized Lyapunov exponents and periodic scanning techniques

Title:
Research on fractal structure of generalized M-J sets utilized Lyapunov exponents and periodic scanning techniques
Authors:
WANG XINGYUAN, CHANG PEIJUN
Source:
Applied mathematics and computation. 175(2):1007-1025
Publisher Information:
New York, NY: Elsevier, 2006.
Publication Year:
2006
Physical Description:
print, 22 ref
Original Material:
INIST-CNRS
Subject Terms:
Control theory, operational research, Automatique, recherche opérationnelle, Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Mesure et intégration, Measure and integration, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Analyse numérique, Numerical analysis, Análisis numérico, Balayage, Scanning, Exploración, Discontinuité, Discontinuity, Discontinuidad, Exposant Lyapunov, Lyapunov exponent, Exponente Lyapunov, Fonction analytique, Analytical function, Función analítica, Fonction variable complexe, Complex variable function, Función variable compleja, Fractale, Fractals, Mathématiques appliquées, Applied mathematics, Matemáticas aplicadas, Méthode expérimentale, Experimental method, Método experimental, Périodicité, Periodicity, Periodicidad, Ensemble Mandelbrot Julia, Mandelbrot Julia set, Inflexibilité topologique, Topological inflexibility, Loi évolution, Evolution law, The generalized M-J sets; Lyapunov exponent; Periodic scanning; Topological inflexibility; Discontinuity evolution law; Fractal, physical meaning
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
School of Electronic and Information Engineering, Dalian University of Technology, Dalian 116024, Liaoning Province, China
ISSN:
0096-3003
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=17689029
Rights:
Copyright 2006 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.17689029
Database:
PASCAL Archive

Further Information

In order to show details of fractal structure of Mandelbrot set precisely, Lyapunov exponents and periodic scanning techniques have been brought forward by Shirriff and Welstead. This paper generalizes these two techniques and puts forward periodicity orbit search and comparison technique which can be used to discuss the relationship of the generalized Mandelbrot-Julia sets (the generalized M-J sets). Adopting the techniques mentioned above and the experimental mathematics method of combining the theory of analytic function of one complex variable with computer aided drawing, this paper researches on the structure topological inflexibility and the discontinuity evolution law of the generalized M-J sets generated from the complex mapping z→zα + c(α ∈ R), and explores structure and distributing of periodicity petal and topological law of periodicity orbits of the generalized M sets, and finds that the generalized M set contains abundant information of structure of the generalized J sets by founding the whole portray of the generalized J sets based on the generalized M set qualitatively. Furthermore, the physical meaning of the generalized M-J sets have been expounded.