Dynamics of polynomial maps over finite fields

01/04/2022

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by   José Alves Oliveira, et al.

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Let 𝔽_q be a finite field with q elements and let n be a positive integer. In this paper, we study the digraph associated to the map x↦ x^n h(x^q-1/m), where h(x)∈𝔽_q[x]. We completely determine the associated functional graph of maps that satisfy a certain condition of regularity. In particular, we provide the functional graphs associated to monomial maps. As a consequence of our results, the number of connected components, length of the cycles and number of fixed points of these class of maps are provided.