Abstract
AbstractWe investigate the relation between the complexity function of a sequence, that is the number p(n) of its factors of length n, and the rank of the associated dynamical system, that is the number of Rokhlin towers required to approximate it. We prove that if the rank is one, then lim , but give examples with lim for any prescribed function G with G (n) = 0(an) for every a > 1. We give exact computations for examples of the ‘staircase’ type, which are strongly mixing systems with quadratic complexity. Conversely, for minimal sequences, if p(n) < an + b for some a ≥ 1, the rank is at most 2[a], with bounded strings of spacers, and the system is generated by a finite number of substitutions.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Reference14 articles.
1. [C] Cassaigne J. . Facteurs spéciaux des suites de complexité sous-affine. Preprint.
2. Equivalence of measure preserving transformations;Ornstein;Mem. Am. Math. Soc.,1982
3. Les transformations de Chacon: combinatoire, structure géométrique, liens avec les systèmes de complexité 2n + 1;Ferenczi;Bull. Soc. Math.,1995
4. Transformations With Discrete Spectrum are Stacking Transformations
Cited by
63 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献