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A cubic polynomial $P$ with a non-repelling fixed point $b$ is said to beimmediately renormalizable if there exists a (connected) QL invariant filledJulia set $K^*$ such that $b\in K^*$. In that case, exactly one critical pointof $P$ does not belong to $K^*$. We show that if, in addition, the Julia set of$P$ has no (pre)periodic cutpoints, then this critical point is recurrent.

Immediate renormalization of cubic complex polynomials with empty rational lamination