G. Álvarez, M. Romera, G. Pastor, F. Montoya, "Determination of Mandelbrot set hyperbolic component centres", Chaos Solitons and Fractals, 9 (1998), 1997-2005. (PDF)

Pau Atela (1992). Bifurcations of dynamic rays in complex polynomials of degree two. Ergodic Theory and Dynamical Systems, 12 , pp 401-423

P. Collet and J. P. Eckmann.

Cowen C C:

Adrien Douady and John H. Hubbard :

Drakopoulos V., Comparing rendering methods for Julia sets , Journal of WSCG 10 (2002), 155–161.

V Dolotin , A Morozow :

V Dolotin , A Morozow :

Ewing John H., Schober Glenn :

Lisa R. Goldberg:

E. N. Gilbert, J. Riordan : Symmetry Types of Periodic Sequences, Illinois J. Math., 5 (December 1961), pp. 657-665, Monograph 2072

S. Grossmann and S. Thomae: "Invariant distributions and stationary correlation functions of one-dimensional discrete processes", Z. Naturforsch. 32a, 1353 (1977)

Bailin HAO : Number of periodic orbits in continuous maps of the interval . Ann. Combin., 4 (2000), 339-346

On Fractal Coloring Techniques by Jussi Härkönen

J. Hubbard and P. Papadopol,:

Irwin Jungreis :

Genadi Levin :

Genadi Levin : Multipliers of periodic orbits of quadratic polynomials and the parameter plane; February 2007) math/0702011

G. Levin, F. Przytycki :

Levin, G. M. :

M. Lutzky :

Abstract: Expressions are given for the number of hyperbolic components, cardioids, and discs which are associated with N-cycles for the Mandelbrot set. We also discuss the distribution of hyperbolic components along the real axis.

Manning A :

Mark McClure :

J. Milnor : "Periodic Orbits, External Rays and the Mandelbrot Set ..."; Asterisque 261 (2000) `Geometrie Complexe et Systemes Dynamiques', pp. 277-333; ims99-3 = [Stony Brook IMS Preprint 1999#3]

Misiurewicz M, Nitecki Z : Combinatorial patterns for maps of the interval , Mem. Amer. Math. Soc. 94 (1991), no. 456

Andrey Morozov : Universal Mandelbrot Set as a Model of Phase Transition Theory (to appear in JETP Lett.) ESI Preprint - (PS , PDF ) 5 pages

J. Milnor and W. Thurston, On Iterated Maps of the Interval, in Dynamical Systems: Proceedings of the special year held at the University of Maryland, College Park, 1986-87, (ed. J. Alexander) Lecture Notes in Math., vol. 1342, Springer-Verlag, Berlin (1988) 465-563.

Lei Tan Similarity between the Mandelbrot set and Julia sets Source: Comm. Math. Phys. 134, no. 3 (1990), 587–617

Tan Lei Voisinages connexes des points de Misiurewicz Annales de l'institut Fourier, 42 no. 4 (1992), p. 707-735

Young Hee Geum, Young Ik Kim :

Young Hee Geum, Young Ik Kim :

Abstract

The governing equation locating component centers in the degree- n bifurcation set is a polynomial with a very high degree and its root-finding lacks numerical accuracy. The equation is transformed to have its degree reduced by a factor (n - 1) . Newton's method applied to the transformed equation improves the accuracy with properly chosen initial values. The numerical implementation is done with Maple V using a large number of computational precision digits. Many cases are studied for 2\leq n \leq 25 and show a remarkably improved computation. Our study extends the results given by Peitgen and Richter [11].

Keywords: Bifurcation; Component Centers; Degree- n Bifurcation Set; Mandelbrot Set; Newton's Method

Warsaw Dynamical Systems Group

Yale fractals group

Department of Mathemathics Technical University of Denmark special thx for recieved papers

arXiv.org owned, operated and funded by Cornell University

The University of California Davis front end for the mathematics arXiv, maintained at Cornell University

eprintweb.org based on arXiv.org

AMS Books Online

Online Mathematics Textbooks collected by George Cain

Stony Brook University Institute for Mathematical Sciences

Experimental Mathematics

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Author: Adam Majewski adammaj1-at-o2-dot-pl

http://republika.pl/fraktal/

2005-07-02