Rigidity and unlikely intersections for stable $p$-adic dynamical systems

Berger asked the question \enquote{To what extent the preperiodic points of a $p$-adic power series determines a stable $p$-adic dynamical system} ? In this work we have applied the preperiodic points of an invertible $p$-adic power series in order to determine the corresponding stable $p$-adic dynamical system.