Vasiga and Shallit [17] study tails and cycles in orbits of iterations of quadratic polynomials over prime fields. These results were extended to repeated exponentiation by Chou and Shparlinski [3]. We show, using the quadratic reciprocity law, that it is possible to extend these results to Rédei functions over prime fields.

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Keywords Cycle structure, One-dimensional dynamics, Redei functions
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Journal Advances in Mathematics of Communications
Qureshi, C. (Claudio), Panario, D, & Martins, R. (Rodrigo). (2017). Cycle structure of iterating redei functions. Advances in Mathematics of Communications, 11(2), 397–407. doi:10.3934/amc.2017034