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arXiv · 1010.5583

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

Fan Ai-Hua·Lingmin Liao
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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.

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Fan Ai-Hua, Lingmin Liao. 2010-10-29. On minimal decomposition of $p$-adic polynomial dynamical systems. https://arxiv.org/abs/1010.5583

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