Geodesic
The adic realization of the Morse transformation and the extension of its action to the solenoid
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamics systems, combinatorial methods. Part XVI, Tome 360 (2008), pp. 70-90

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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. Bibl. – 14 titles. 
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     title = {The adic realization of the {Morse} transformation and the extension of its action to the solenoid},
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A. M. Vershik; B. Solomyak. The adic realization of the Morse transformation and the extension of its action to the solenoid. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamics systems, combinatorial methods. Part XVI, Tome 360 (2008), pp. 70-90. http://geodesic.mathdoc.fr/item/ZNSL_2008_360_a2/