Wiman–Valiron Discs and the Dimension of Julia Sets

Waterman, James (2021). Wiman–Valiron Discs and the Dimension of Julia Sets. International Mathematics Research Notices, 2021(12), 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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