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September  2009, 25(3): 777-795. doi: 10.3934/dcds.2009.25.777

Minimal dynamical systems on a discrete valuation domain

Jean-Luc Chabert 1, , Ai-Hua Fan 1, and  Youssef Fares 1,

1. 

LAMFA, UMR 6140, CNRS, University of Picardie, 33 Rue Saint Leu, 80039 Amiens, France, France, France

Received  July 2008 Revised  February 2009 Published  August 2009

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.
Keywords: discrete dynamics, discrete valuation domain..
Mathematics Subject Classification: Primary: 37B05; Secondary: 11K3.
Citation: Jean-Luc Chabert, Ai-Hua Fan, Youssef Fares. Minimal dynamical systems on a discrete valuation domain. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 777-795. doi: 10.3934/dcds.2009.25.777
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