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Minimal dynamical systems on a discrete valuation domain
We consider isometric dynamical systems on a Legendre set of a
discrete valuation domain with finite residual field. We
characterize the minimality of the system by using the structure
sequence of the Legendre set and also find the corresponding adding
machine to which such a minimal system is conjugate. The minimality
of affine maps acting on the domain or on the group of units is
fully studied.