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The adic realization of the Morse transformation and the extension of its action to the solenoid. (English. Russian original) Zbl 1303.37004

J. Math. Sci., New York 158, No. 6, 809-818 (2009); translation from Zap. Nauchn. Semin. POMI 360, 70-90 (2008).
Summary: We consider the adic realization of the Morse transformation on the additive group of integer dyadic numbers. We discuss the arithmetic properties of this action. Then we extend this action to an action of the group of rational dyadic numbers on the solenoid.

MSC:

37B10 Symbolic dynamics
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
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