Julia sets with a wandering branching point
Buff, Xavier (Université Paul Sabatier. Institut de Mathématiques de Toulouse (France))
Canela Sánchez, Jordi (Université Paris-Est Marne-La-Vallée. Laboratoire d'Analyse et de Mathématiques Apliquées (France))
Roesch, Pascale (Université Paul Sabatier. Institut de Mathématiques de Toulouse (France))

Date:	2020
Abstract:	According to the Thurston No Wandering Triangle Theorem, a branching point in a locally connected quadratic Julia set is either preperiodic or precritical. Blokh and Oversteegen proved that this theorem does not hold for higher degree Julia sets: there exist cubic polynomials whose Julia set is a locally connected dendrite with a branching point which is neither preperiodic nor precritical. In this article, we reprove this result, constructing such cubic polynomials as limits of cubic polynomials for which one critical point eventually maps to the other critical point which eventually maps to a repelling fixed point.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió sotmesa a revisió
Published in:	Indiana University mathematics journal, Vol. 69, Issue 6 (2020) , p. 2241-2265, ISSN 0022-2518

DOI: 10.1512/iumj.2020.69.8056

Preprint 21 p, 1.6 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles