Cutpoints of invariant subcontinua of polynomial Julia sets

2020/10/01 by Alexander Blokh, Blokh, Alexander, Lex Oversteegen +3 · 1 citation
Mathematics · #37F20 #37F50 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37F45 #Secondary 37F10 #math.DS #msc:37F10 #msc:37F20 #msc:37F45 #msc:37F50

paper · pdf · doi:10.48550/arxiv.2010.00419

17 pages

arxiv created 2021/01/20 · arxiv updated 2021/01/21

Abstract

We prove fixed point results for branched covering maps f of the plane. For complex polynomials P with Julia set J_P these imply that periodic cutpoints of some invariant subcontinua of J_P are also cutpoints of J_P. We deduce that, under certain assumptions on invariant subcontinua Q of J_P, every Riemann ray to Q landing at a periodic repelling/parabolic point x∈ Q is isotopic to a Riemann ray to J_P relative to Q.

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