On postcritical sets of quadratic polynomials with a neutral fixed point

2024/07/19 by Hongyu Qu, Qu, Hongyu
Mathematics · #Advanced Differential Equations and Dynamical Systems #Iterative Methods for Nonlinear Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2407.14476

Abstract

The control of postcritical sets of quadratic polynomials with a neutral fixed point is a main ingredient in the remarkable work of Buff and Chéritat to construct quadratic Julia sets with positive area. Based on the Inou-Shishikura theory, they obtained the control for the case of rotation numbers of bounded high type. Later, Cheraghi developed several elaborate analytic techniques based on Inou-Shishikura's results and obtained the control for the case of rotation numbers of high type. In this paper, based on the pseudo-Siegel disk theory of Dudko and Lyubich, we obtained the control for the general case.

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