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Compact Automata

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1294)

Abstract

If now A is a compact metric set and if Φ01,…,Φ q−1 are q continuous maps from A into A (q ≥ 2), it is easy to define the automatic action of the family (Φ j ) on A, and to exhibit, in this way, automatic sequences taking their values in the compact set A. Such an example is given by the sequence (e 2iπαSq(n)), where S q (n), as usual, denotes the sum of digits in the q-adic expansion of n, andwhere α is any irrational number.

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Correspondence to Martine Queffélec .

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© 2010 Springer-Verlag Berlin Heidelberg

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Queffélec, M. (2010). Compact Automata. In: Substitution Dynamical Systems - Spectral Analysis. Lecture Notes in Mathematics(), vol 1294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11212-6_12

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