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Minimal dynamical systems on a discrete valuation domain

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  • 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.
    Mathematics Subject Classification: Primary: 37B05; Secondary: 11K36.

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