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2000 | 164 | 1 | 41-60
Tytuł artykułu

Trees of visible components in the Mandelbrot set

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We discuss the tree structures of the sublimbs of the Mandelbrot set M, using internal addresses of hyperbolic components. We find a counterexample to a conjecture by Eike Lau and Dierk Schleicher concerning topological equivalence between different trees of visible components, and give a new proof to a theorem of theirs concerning the periods of hyperbolic components in various trees.
Słowa kluczowe
Rocznik
Tom
164
Numer
1
Strony
41-60
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-04-27
poprawiono
2000-01-18
Twórcy
autor
  • Department of Mathematics, University of Jyväskylä, P.O. Box 35, 40351 Jyväskylä, Finland, virpik@math.jyu.fi
Bibliografia
  • [At] P. Atela, Bifurcations of dynamic rays in complex polynomials of degree two, Ergodic Theory Dynam. Systems 12 (1991), 401-423.
  • [Be] A. F. Beardon, Iteration of Rational Functions, Complex Analytic Dynamical Systems, Grad. Texts in Math. 132, Springer, 1991.
  • [BK] C. Bandt and K. Keller, Symbolic dynamics for angle-doubling on the circle II: Symbolic description of the abstract Mandelbrot set, Nonlinearity 6 (1993), 377-392.
  • [BS] H. Bruin and D. Schleicher, Symbolic Dynamics of Quadratic Polynomials, in preparation.
  • [CG] L. Carleson and T. W. Gamelin, Complex Dynamics, Universitext, Springer, 1993.
  • [K1] K. Keller, Correspondence and translation principles for the Mandelbrot set, preprint #14, Institute for Mathematical Sciences, Stony Brook, 1997.
  • [K2] K. Keller, Errata for Correspondence and translation principles for the Mandelbrot set', http://www.math-inf.uni-greifswald.de/~keller/research.html.
  • [LS] E. Lau and D. Schleicher, Internal addresses in the Mandelbrot set and irreducibility of polynomials, preprint #19, Institute for Mathematical Sciences, Stony Brook, 1994,
  • [La] P. Lavaurs, Une description combinatoire de l'involution définie par M sur les rationnels à dénominateur impair, C. R. Acad. Sci. Paris 303 (1986), 143-146.
  • [Mi] J. Milnor, Periodic orbits, external rays, and the Mandelbrot set; an expository account, preprint #3, Institute for Mathematical Sciences, Stony Brook, 1999.
  • [Pe] C. Penrose, Quotients of the shift associated with dendrite Julia sets of quadratic polynomials, Ph.D. thesis, Warwick, 1990.
  • [S1] D. Schleicher, Internal addresses in the Mandelbrot set and irreducibility of polynomials, Ph.D. thesis, Cornell Univ., 1994.
  • [S2] D. Schleicher, Rational parameter rays of the Mandelbrot set, preprint #13, Institute for Mathematical Sciences, Stony Brook, 1997.
  • [Th] W. Thurston, On the geometry and dynamics of iterated rational maps, preprint, Princeton Univ., 1985.
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Bibliografia
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bwmeta1.element.bwnjournal-article-fmv164i1p41bwm
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