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arXiv · 1309.6598

Combinatorics of cycle lengths on Wehler K3 Surfaces over finite fields

Joao Alberto de Faria·Benjamin Hutz
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Abstract

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

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Joao Alberto de Faria, Benjamin Hutz. 2013-09-25. Combinatorics of cycle lengths on Wehler K3 Surfaces over finite fields. https://arxiv.org/abs/1309.6598

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