The Graph Structure of Chebyshev Polynomials over Finite Fields and Applications

2018/03/17 by Qureshi, Claudio, Panario, Daniel · 2 citations
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.06539

Abstract

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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• Partitioning ℤ_sp in finite fields and groups of trees and cycles
• Periodicity and Dynamical Systems of Dickson Polynomials in Finite Fields

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