Activity measures of dynamical systems over non-archimedean fields

Toward the understanding of bifurcation phenomena of dynamics on the Berkovich projective line P1,an over non-archimedean fields, we study the stability (or passivity) of critical points of families of rational functions parametrized by analytic curves. We construct the activity measure of a critical point of a family of rational functions, and study its properties. For a family of polynomials, we analyze the support of the activity measure, for example its relation to boundedness locus, i.e., the Mandelbrot set, and to the normality of the sequence of the forward orbit.