English

On postcritical sets of quadratic polynomials with a neutral fixed point

Dynamical Systems 2024-07-25 v2 Complex Variables

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 Ch\'eritat 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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Cite

@article{arxiv.2407.14476,
  title  = {On postcritical sets of quadratic polynomials with a neutral fixed point},
  author = {Hongyu Qu},
  journal= {arXiv preprint arXiv:2407.14476},
  year   = {2024}
}

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17 pages