Combinatorics of Cycle Lengths on Wehler K3 Surfaces Over Finite Fields

From NZJM

Jump to: navigation, search

New Zealand Journal of Mathematics

Vol. 45, (2015), Pages 19-31


João Alberto de Faria

Department of Mathematical Sciences

Florida Institute of Technology

150 W. University Blvd

Melbourne, FL 32901

mailto:jdefaria2010@my.fit.edu

Benjamin Hutz

Department of Mathematical Sciences

Florida Institute of Technology

150 W. University Blvd

Melbourne, FL 32901

mailto:bhutz@fit.edu




Abstract We study the dynamics of maps arising from the composition of two non-commuting involutions 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.

Keywords Wehler K3 surface, reversible maps, dynamical systems, cycle lengths.

Classification (MSC2000) 37P55, 37E30, 37C80, 11T99.

Full text

Full paper

Personal tools