The landing of parameter rays at non-recurrent critical portraits

Abstract

Based on the distortion theory developed by Cui-Tan [5], we prove the landing of every parameter ray at critical portraits coming from non-recurrent polynomials, thereby generalizing a result of Kiwi [8, Corollary].

On rational maps with buried critical points

“…We normalize φ 0,r such that it fixes a 1 , a 2 , a 3 . Lemma 2.4 implies that such normalized rational maps R r still belong to H. By [Gao19, Proposition 3.3] or by similar arguments in [GZ18, Step IV of the proof of Theorem 1.1], the rational maps R r uniformly converge to f as r → 0, which implies f ∈ ∂H.…”

On the core entropy of Newton maps

“…This surgery will be used to construct sequences of polynomials or Newton maps on which the entropy function achieving the inferior (in the proof of Proposition 1.2 and Theorem 1.3). A similar idea is used in [CT3,GZ] for a very special case.…”