Patrick Ingram, York University
“The critical height of a rational function”
In complex holomorphic dynamics, the orbits of the critical points of a rational function play a special role. Silverman proposed a measure of complexity of a rational function defined over a number field, the “critical height”, which measures the rate of growth of the Weil height along the critical orbits. We will survey some recent work on Silverman’s critical height, and in particular show that it is at least roughly an ample Weil height on the moduli space of rational functions of a given degree.
M3-3103