title: Arithmetical method to detect integrability in maps.
abstract: We develop a method to detect the presence of integrals of the motion in symplectic rational maps, by representing these maps over finite fields and examining their orbit structure. We find markedly different orbit statistics depending upon whether the map is integrable or not.
authors.affiliation: School of Mathematics, The University of New South Wales, Sydney NSW 2052, Australia.
authors.forename: J A G
authors.initials: JA
authors.lastname: Roberts
authors.forename: F
authors.initials: F
authors.lastname: Vivaldi