On the pullback relation on curves induced by a Thurston map

2021/02/24 by Pilgrim, Kevin M. · 2 citations
#37F20 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.12402

Abstract

Via taking connected components of preimages, a Thurston map f: (S², P_f) → (S², P_f) induces a pullback relation on the set of isotopy classes of curves in the complement of its postcritical set P_f. We survey known results about the dynamics of this relation, and pose some questions.

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• On the Global Curve Attractor for polynomial gluing
• Rational maps with constant Thurston pullback mapping

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