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.