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Algorithms for
classifying points in a 2-adic Mandelbrot set
Brandon Bate, Kyle Craft and Jonathon Yuly
Vol. 12 (2019), No. 6, 969–994
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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. |
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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Authors |
| Brandon Bate | |
| Department of Mathematics Houghton College Houghton, NY United States |
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| Kyle Craft | |
| Houghton College Houghton, NY United States |
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| Jonathon Yuly | |
| Houghton College Houghton, NY United States |
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