On minimal decomposition of p-adic polynomial dynamical systems

2010/10/27 by Fan Ai-Hua, Ai-Hua, Fan, Lingmin Liao +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT

paper · pdf · doi:10.48550/arxiv.1010.5583

27 pages

arxiv created 2010/10/29 · arxiv updated 2010/11/01

Abstract

A polynomial of degree ≥ 2 with coefficients in the ring of p-adic numbers ℤ_p is studied as a dynamical system on 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 ℤ₂, we exhibit all its minimal subsystems.

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