Displaying similar documents to “Dynamics on Hubbard trees”

Existence of quadratic Hubbard trees

Henk Bruin, Alexandra Kaffl, Dierk Schleicher (2009)

Fundamenta Mathematicae

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A (quadratic) Hubbard tree is an invariant tree connecting the critical orbit within the Julia set of a postcritically finite (quadratic) polynomial. It is easy to read off the kneading sequences from a quadratic Hubbard tree; the result in this paper handles the converse direction. Not every sequence on two symbols is realized as the kneading sequence of a real or complex quadratic polynomial. Milnor and Thurston classified all real-admissible sequences, and we give a classification...

Hubbard trees

Alfredo Poirier (2010)

Fundamenta Mathematicae

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We provide a full classification of postcritically finite polynomials as dynamical systems by means of Hubbard trees. The information encoded in these objects is solid enough to allow us recover all the relevant statical and dynamical aspects of the corresponding Julia sets.

Conservative polynomials and yet another action of Gal ( ℚ ¯ / ℚ ) on plane trees

Fedor Pakovich (2008)

Journal de Théorie des Nombres de Bordeaux

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In this paper we study an action D of the absolute Galois group Γ = Gal ( ℚ ¯ / ℚ ) on bicolored plane trees. In distinction with the similar action provided by the Grothendieck theory of “Dessins d’enfants” the action D is induced by the action of Γ on equivalence classes of conservative polynomials which are the simplest examples of postcritically finite rational functions. We establish some basic properties of the action D and compare it with the Grothendieck action.