Abstract
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.
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Fan, AH., Fares, Y. Minimal subsystems of affine dynamics on local fields. Arch. Math. 96, 423–434 (2011). https://doi.org/10.1007/s00013-011-0245-2
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DOI: https://doi.org/10.1007/s00013-011-0245-2