Mathematics > Dynamical Systems
[Submitted on 5 Jun 2023
(this version)
, latest version 21 Jul 2023 (v2)
]
Title: On hyperbolic dimension gap for entire functions
Title: 关于整函数的双曲维数间隙
Abstract: Polynomials and entire functions whose hyperbolic dimension is strictly smaller than the Hausdorff dimension of their Julia set are known to exist but in all these examples the latter dimension is maximal, i.e. equal to two. In this paper we show that there exist hyperbolic entire functions $f$ having Hausdorff dimension of the Julia set $\HD (\J _f)<2$ and hyperbolic dimension $\HypDim(f)<\HD(\J_f)$.
Submission history
From: Volker Mayer [view email][v1] Mon, 5 Jun 2023 06:54:10 UTC (15 KB)
[v2] Fri, 21 Jul 2023 06:31:53 UTC (15 KB)
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