Invariant Spanning Trees for Quadratic Rational Maps

  • Anastasia Shepelevtseva
  • Vladlen TimorinEmail author
Research Contribution


We study Thurston equivalence classes of quadratic post-critically finite branched coverings. For these maps, we introduce and study invariant spanning trees. We give a computational procedure for searching for invariant spanning trees. This procedure uses bisets over the fundamental group of a punctured sphere. We also introduce a new combinatorial invariant of Thurston classes—the ivy graph.


Complex dynamics Invariant tree Iterated monodromy group 

Mathematics Subject Classification

Primary 37F20 Secondary 37F10 



The authors are grateful to D. Dudko and M. Hlushchanka for useful discussions, to D. Schleicher and Jacobs University Bremen for hospitality and inspiring working conditions during the workshop “Dynamics, Geometry and Groups” in May 2017, where these and other enlightening discussions took place. We are also grateful to the referee for valuable remarks and suggestions.


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Copyright information

© Institute for Mathematical Sciences (IMS), Stony Brook University, NY 2019

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia
  2. 2.Scuola Normale SuperiorePisaItaly

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