ARITHMETIC DYNAMICS AND DYNAMICAL UNITS

Abstract

For a point of order two and a point of order three for a rational

function defined over a number field with good reduction outside a set

S, it is known that the bilinear form B([x1, y1], [x2, y2]) = x1y2 − x2y1

yields a unit in the ring of S-integers of a number field. We prove that

this is essentially the only bilinear form with this property