This article is dedicated to the study of dynamical systems over the field of p -adic numbers in higher dimension, defined by a specific monomial function in each component. We determine a condition on the Jacobian matrix for a point to be an attractor of the system. We also found basins of attraction and centers of Siegel disks in terms of basins of attraction and Siegel disks of its components, respectively.
Galeano-Peñaloza et al. (Sun,) studied this question.