In this work we study the forward filled Julia sets of a class of p -adic polynomial maps f: Qₚ² Qₚ² defined by f (x, y) = (xy+c, x), where cₚ is a p -adic number. In particular, we prove that if |c|1, then we exhibit a bounded set such that, the filled Julia set is characterized by the points whose the orbit enter in this set and it never leaves it after each iteration of the map f. Moreover, for all parameter c, we prove that both coordinates of the orbit of all points that are not in the filled Julia set goes to infinity in p -adic norm.
Bastos et al. (Sun,) studied this question.