$p$-adic dynamical systems of the function $a x^{-2}$

Abstract

In this paper we study p-adic dynamical systems generated by the function f (x) = a x 2 in the set of complex p-adic numbers. We find an explicit formula for the n-fold composition of f for any n ≥ 1. Using this formula we give fixed points, periodic points, basin of attraction and Siegel disk of each fixed (periodic) point depending on parameters p and a.