In this chapter, we will study symbolic sequences generated by an irrational rotation. Such sequences appear each time a dynamical system has two rationally independent periods; this is a very typical situation, arising for example in astronomy (with the rotation of the moon around the earth, and of the earth around the sun), or in music (with the building of musical scales, related to the properties of log 3/log 2), and such sequences have been studied for a long time. These sequences, or related objects, appear in the mathematical literature under many different names: rotation sequences, cutting sequences, Christoffel words, Beatty sequences, characteristic sequences, balanced sequences, Sturmian sequences, and so on.
KeywordsCode Sequence Initial Letter Continue Fraction Expansion Admissible Sequence Markov Partition
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