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We study the dynamics of maps arising from the composition of twonon-commuting involution on a K3 surface. These maps are a particular exampleof reversible maps, i.e., maps with a time reversing symmetry. Thecombinatorics of the cycle distribution of two non-commuting involutions on afinite phase space was studied by Roberts and Vivaldi. We show that thedynamical systems of these K3 surfaces satisfy the hypotheses of their results,providing a description of the cycle distribution of the rational points overfinite fields. Furthermore, we extend the involutions to include the case wherethere are degenerate fibers and prove a description of the cycle distributionin this more general situation.

Combinatorics of cycle lengths on Wehler K3 Surfaces over finite fields