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Toward the understanding of bifurcation phenomena of dynamics on theBerkovich projective line $\mathbb{P}^{1,an}$ over non-archimedean fields, westudy the stability (or passivity) of critical points of families ofpolynomials parametrized by analytic curves. We construct the activity measureof a critical point of a family of rational functions, and study itsproperties. For a family of polynomials, we study more about the activity locussuch as its relation to boundedness locus, i.e., the Mandelbrot set, and to thenormality of the sequence of the forward orbit.

Activity measures of dynamical systems over non-archimedean fields