We completely describe the functional graph associated to iterations of Chebyshev polynomials over finite fields. Then, we use our structural results to obtain estimates for the average rho length, average number of connected components and the expected value for the period and preperiod of iterating Chebyshev polynomials.

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Keywords Chebyshev polynomials, Dynamical systems over finite fields, Permutation polynomials over finite fields
Persistent URL dx.doi.org/10.1007/s10623-018-0545-7
Journal Designs, Codes and Cryptography
Qureshi, C. (Claudio), & Panario, D. (2018). The graph structure of Chebyshev polynomials over finite fields and applications. Designs, Codes and Cryptography. doi:10.1007/s10623-018-0545-7