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Periodic points
and tail lengths of split polynomial maps modulo primes
Benjamin Hutz and Teerth Patel
Vol. 15 (2022), No. 2, 185–206
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Abstract |
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Explicit formulas are obtained for the number of periodic points and maximum tail length of split polynomial maps over finite fields for affine and projective space. This work includes a detailed analysis of the structure of the directed graph over finite fields for Chebyshev polynomials of nonprime degree in dimension 1 and the powering map in any dimension. The results are applied to provide an algorithm for determining the type of a given map defined over the rational numbers through analysis of its cycle statistics modulo primes. |
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Keywords
functional graph, periodic points, Chebyshev polynomial,
power map
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Mathematical Subject Classification 2010
Primary: 37P25, 37P35
Secondary: 11B50
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Milestones
Received: 11 September 2018
Revised: 28 July 2021
Accepted: 27 August 2021
Published: 29 July 2022
Communicated by Kenneth S. Berenhaut
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Authors |
| Benjamin Hutz | |
| Department of Mathematics and
Statistics Saint Louis University St. Louis, MO United States |
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| Teerth Patel | |
| Saint Louis University St. Louis, MO United States |
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