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.
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