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2000 | 164 | 2 | 115-141
Tytuł artykułu

Dynamics on Hubbard trees

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
It is well known that the Hubbard tree of a postcritically finite complex polynomial contains all the combinatorial information on the polynomial. In fact, an abstract Hubbard tree as defined in [23] uniquely determines the polynomial up to affine conjugation. In this paper we give necessary and sufficient conditions enabling one to deduce directly from the restriction of a quadratic Misiurewicz polynomial to its Hubbard tree whether the polynomial is renormalizable, and in this case, of which type. Moreover, we study dynamical features such as entropy, transitivity or periodic structure of the polynomial restricted to the Hubbard tree, and compare them with the properties of the polynomial on its Julia set. In other words, we want to study how much of the "dynamical information" about the polynomial is captured by the Hubbard tree.
Rocznik
Tom
164
Numer
2
Strony
115-141
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-04-25
poprawiono
2000-01-28
Twórcy
  • Departament de Matemàtiques, Facultat de Ciències (Edifici Cc), Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain, alseda@mat.uab.es
  • Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain, fagella@maia.ub.es
Bibliografia
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  • [3] Ll. Alsedà, S. Kolyada, J. Llibre and Ľ. Snoha, Entropy and periodic points for transitive maps, Trans. Amer. Math. Soc. 351 (1999), 1551-1573.
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  • [19] C. T. McMullen, Complex Dynamics and Renormalization, Princeton Univ. Press, 1994.
  • [20] J. Milnor, Dynamics in One Complex Variable: Introductory Lectures, Vieweg, 1999.
  • [21] J. Milnor, Local connectivity of Julia sets: expository lectures, Stony Brook preprint no. 1990/5 (1992).
  • [22] C. L. Petersen, On the Pommerenke-Levin-Yoccoz inequality, Ergodic Theory Dynam. Systems 13 (1993), 785-806.
  • [23] A. Poirier, On postcritically finite polynomials. Part two: Hubbard trees, Stony Brook preprint no. 1993/7.
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  • [26] P. Walters, An Introduction to Ergodic Theory, Grad. Texts in Math. 79, Springer, New York, 1982.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-fmv164i2p115bwm
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