Cutpoints of Invariant Subcontinua of Polynomial Julia Sets

Autor: Vladlen Timorin, Alexander Blokh, Lex Oversteegen
Rok vydání: 2021
Předmět:
Zdroj: Arnold Mathematical Journal. 8:271-284
ISSN: 2199-6806
2199-6792
DOI: 10.1007/s40598-021-00186-8
Popis: 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 $$x\in Q$$ is isotopic to a Riemann ray to $$J_{P}$$ relative to Q.
Databáze: OpenAIRE
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