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

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

2010-10-27

arxiv.org/abs/1010.5583v2

Mathematics

Dynamical Systems

27 pages

Scientific paper

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.

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