Perturbation of a p-adic dynamical system in two variables

In this work the authors study the perturbed dynamical system F-qr in Q(p) x Q(p) defined by (x, y) -> F-qr(x, y) = (x(m), y(n)) + (q(x, y), r(x, y)) where m,n E is an element of N, m >= 2, n >= 2 and the perturbation terms, q(x, y) and r(x,y), are polynomials whose coefficients have small p-adic valuation. They give sufficient conditions on the perturbation terms in order to have a one to one correspondence between fixed points of the non perturbed system F(x, y) = (x(m), y(n)) and of the perturbed one. They also describe the behavior of iterations of points near the fixed points of F-qr, showing preservation of the nature of some fixed points of F.