Given a family $\{ f_{ \lambda} \}_{ \lambda \in \Lambda}$ of polynomial maps of degree $d$ where $\Lambda$ is the set of parameters, a polynomial map $f_{ \lambda_0}$ is called { \it $J$-stable in $\Lambda$} if there exists a neighborhood of $\lambda_0$ in $\Lambda$ such that for any element $\lambda$ in the neighborhood, there exists a conjugacy between the dynamics on the Julia sets of $f_\lambda$ and $f_{ \lambda_0}$. The aim of this paper is to show that a polynomial map $f_{ \lambda_0}$ over the field $\mathbb{ C}_p$ of $p$-adic complex numbers is $J$-stable in the family of polynomial maps over $\mathbb{ C}_p$ if $f_{ \lambda_0}$ is { \it immediately expanding}.
Categories: math.DS