The adic realization of the Morse transformation and the extension of its action on the solenoid
A. Vershik, B. Solomyak
TL;DR
This paper explores the adic realization of the Morse transformation on dyadic integers, examines its arithmetic properties, and extends its action to the group of rational dyadic numbers on the solenoid.
Contribution
It introduces a novel extension of the Morse transformation action from dyadic integers to rational dyadic numbers on the solenoid.
Findings
Characterization of the Morse transformation's arithmetic properties
Extension of the action to the group of rational dyadic numbers
Insights into the structure of the solenoid under this extended action
Abstract
We consider the adic realization of the Morse transformation on the additive group of integer dyadic numbers. We discuss the arithmetic properties of that action. Then we extend that action to the action of the group of rational dyadic numbers on the solenoid.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Geometric and Algebraic Topology · semigroups and automata theory