Minimal subsystems of affine dynamics on local fields. (English) Zbl 1214.11134

Summary: We describe the dynamics of an arbitrary affine dynamical system on a local field by exhibiting all its minimal subsystems. In the special case of the field \({\mathbb{Q}_p}\) of \(p\)-adic numbers, for any non-trivial affine dynamical system, we prove that the field \({\mathbb{Q}_p}\) is decomposed into a countable number of invariant balls or spheres each of which consists of a finite number of minimal subsets. Consequently, we give a complete classification of topological conjugacy for non-trivial affine dynamics on \({\mathbb{Q}_p}\). For each given prime \(p\), there is a finite number of conjugacy classes.


11S82 Non-Archimedean dynamical systems
37P20 Dynamical systems over non-Archimedean local ground fields
Full Text: DOI


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