Dynamics on Hubbard trees

Lluís Alsedà, Núria Fagella

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)115-141
JournalFundamenta Mathematicae
Volume164
Issue number2
Publication statusPublished - 1 Dec 2000

Keywords

  • Hubbard trees
  • Misiurewicz polynomials
  • Renormalization
  • Topological entropy
  • Transitivity

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