The landing of parameter rays at non-recurrent critical portraits

TL;DR

This paper proves that parameter rays land at non-recurrent critical portraits in polynomial parameter spaces, extending previous results and utilizing distortion theory to establish the landing behavior.

Contribution

It generalizes Kiwi's result by proving landing of parameter rays at non-recurrent critical portraits using distortion theory.

Findings

Parameter rays land at non-recurrent critical portraits.

The result extends previous work by Kiwi.

Distortion theory is effectively applied to polynomial parameter spaces.

Abstract

Based on the distortion theory developed by Cui--Tan \cite{CT15}, we prove the landing of every parameter ray at critical portraits coming from non-recurrent polynomials, thereby generalizing a result of Kiwi \cite[Corollary]{Ki05}