Periodic points and tail lengths of split polynomial maps modulo primes
Dynamical Systems
2022-08-10 v1
Abstract
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 for Chebyshev polynomials of non-prime degree in dimension 1 and the powering map in any dimension. The results are applied to an algorithm for determining the type of a given map through analysis of its cycle statistics modulo primes.
Cite
@article{arxiv.1710.07821,
title = {Periodic points and tail lengths of split polynomial maps modulo primes},
author = {Benjamin Hutz and Teerth Patel},
journal= {arXiv preprint arXiv:1710.07821},
year = {2022}
}
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14 pages