Asymptotic behavior of arithmetic equivariants in non-archimedean dynamics

Rumely recently introduced three arithmetic equivariants attached to a rational map $phi$ over a non-Archimedean field. The first is a function $ordRes_phi:pberk to RR$ carrying information about the resultant of various conjugates of $phi$. The second is the set of points where $ordRes_phi$ is minimized; in the case that $phi$ has potential good reduction, this set identifies the conjugate $phi^gamma$ at which $phi$ attains good reduction. The third object is a measure $nu_phi$, a weighted sum of finitely many points in the hyperbolic Berkovich line; the weights are determined by local geometric properties of the map $phi$. In this dissertation, we study the asymptotic behavior of the corresponding objects attached to the iterates of $phi$.