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Abstract
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In her Ph.D. thesis, Jacqueline Anderson identified a nonarchimedean set similar in
spirit to the Mandelbrot set which appears to exhibit a fractal-like boundary. We
continue this research by presenting algorithms for determining when rational points
lie in this set. We then prove that certain infinite families of points lie in (or
out) of this set, giving greater resolution to the self-similarity present in
this set.
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Keywords
$p$-adic Mandelbrot set, nonarchimedean dynamical systems
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Mathematical Subject Classification 2010
Primary: 37P05, 11S82
Secondary: 11Y99
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Milestones
Received: 27 July 2018
Revised: 8 January 2019
Accepted: 18 February 2019
Published: 3 August 2019
Communicated by Kenneth S. Berenhaut
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