Cutpoints of Invariant Subcontinua of Polynomial Julia Sets
Autor: | Vladlen Timorin, Alexander Blokh, Lex Oversteegen |
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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 |
Externí odkaz: |
Abstrakt: | 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. |
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ISSN: | 21996806 21996792 |
DOI: | 10.1007/s40598-021-00186-8 |