On chaos of a cubic $p$-adic dynamical system

Abstract

In the paper we describe basin of attraction of the $p$-adic dynamical system $f(x)=x^3+a{x}^2$. Moreover, we also describe the Siegel discs of the system, since the structure of the orbits of the system is related to the geometry of the $p$-adic Siegel discs.

10 pages