Wiman–Valiron Discs and the Dimension of Julia Sets

Waterman, James (2020). Wiman–Valiron Discs and the Dimension of Julia Sets. International Mathematics Research Notices, article no. rnaa029.

DOI: https://doi.org/10.1093/imrn/rnaa029

Abstract

We show that the Hausdorff dimension of the set of points of bounded orbit in the Julia set of a meromorphic map with a simply connected direct tract and a certain restriction on the singular values is strictly greater than one. This result is obtained by proving new results related to Wiman–Valiron theory.

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• Item ORO ID
• 69807
• Item Type
• Journal Item
• ISSN
• 1687-0247
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2020 The Authors
• Related URLs
• • https://arxiv.org/abs/1910.08474(Other)
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