Hausdorff dimension in quasiregular dynamics
Walter Bergweiler, Athanasios Tsantaris
TL;DR
This paper investigates the Hausdorff dimension of the fast escaping set and Julia set in quasiregular dynamics on three-dimensional space, revealing that the former can vary continuously within a specific range.
Contribution
It demonstrates that the Hausdorff dimension of the fast escaping set can be any value between 1 and 3 for quasiregular maps in three dimensions.
Findings
Hausdorff dimension of fast escaping set can be any in [1,3]
Estimates for Hausdorff dimension of Julia set under growth conditions
Provides new insights into the structure of quasiregular dynamical systems
Abstract
It is shown that the Hausdorff dimension of the fast escaping set of a quasiregular self-map of can take any value in the interval . The Hausdorff dimension of the Julia set of such a map is estimated under some growth condition.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Differential Equations and Dynamical Systems · Quantum chaos and dynamical systems