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Abstract
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We construct a geometrically self-similar Cantor set
of
genus
in
.
This construction is the first for which the local genus is shown to be
at every
point of
.
As an application, we construct, also for the first time, a uniformly quasiregular mapping
for which
the Julia set
is a genus
Cantor set.
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Keywords
Cantor sets, Julia sets, uniformly quasiregular mappings
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Mathematical Subject Classification
Primary: 54C50
Secondary: 30C65, 37F10, 37F50
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Milestones
Received: 25 August 2021
Revised: 31 October 2022
Accepted: 5 November 2022
Published: 21 March 2023
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Publishers). |
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