On minimal decomposition of $p$-adic polynomial dynamical systems

Abstract

A polynomial of degree $\ge 2$ with coefficients in the ring of $p$-adic numbers ${\mathbb{Z}}_p$ is studied as a dynamical system on ${\mathbb{Z}}_p$. It is proved that the dynamical behavior of such a system is totally described by its minimal subsystems. For an arbitrary quadratic polynomial on ${\mathbb{Z}}_2$, we exhibit all its minimal subsystems.

arXiv comment27 pages