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Inverse problems of symbolic dynamics. (Russian. English summary) Zbl 0868.58023

Summary: Let \(P(n)\) be a polynomial with irrational greatest coefficient. Let also a superword \(W\) \((W=(w_n)\), \(n\in \mathbb{N})\) be the sequence of first binary digits of \(\{P(n)\}\), i.e., \(w_n=[2\{P(n)\}]\), and \(T(k)\) be the number of different subwords of \(W\) whose length is equal to \(k\). The main result of the paper is the following:
Theorem 1.1. For any \(n\) there exists a polynomial \(Q(k)\) such that if \(\text{deg}(P)=n\), then \(T(k)=Q(k)\) for all sufficiently large \(k\).

MSC:

37E99 Low-dimensional dynamical systems
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