Dynamics of convergent power series on the integral ring of a finite extension of \Qp

2014/01/06 by Shilei Fan, Fan, Shilei, Lingmin Liao +1
Computer Science · Mathematics · #11S82 (Secondary) #37B05 #37P10 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Topological and Geometric Data Analysis #advanced mathematical theories #math.DS #math.NT #msc:11S82 #msc:37B05 #msc:37P10

paper · pdf · doi:10.48550/arxiv.1401.1062

18pages

openalex publication_date 2014/01/06 · arxiv created 2014/08/08 · arxiv updated 2014/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a finite extension of the field ℚ_p of p-adic numbers and Ø be its integral ring. The convergent power series with coefficients in Ø are studied as dynamical systems on Ø. A minimal decomposition theorem for such a dynamical system is obtained. It is proved that there are uncountably many minimal subsystems, provided that there is a minimal set consisting of infinitely many points. In particular, the complete detailed minimal decompositions of all affine systems are derived.

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