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Register a new userCutpoints of invariant subcontinua of polynomial Julia sets
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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 $xin Q$ is isotopic to a Riemann ray to $J_P$ relative to $Q$.
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