Abstract
In this chapter, we recall elementary facts on topological dynamical systems, and we focus later on a particular case of such systems naturally associated with a bounded sequence. When the sequence takes its values in a finite set, we give an explicit characterization of the dynamical properties of the system. The last section is devoted to the spectral study of sequences with the aid of correlation measures, and to a quick survey on uniform distribution and related sets of integers.
Keywords
- Bounded Sequence
- Correlation Measure
- Invariant Probability Measure
- Irrational Rotation
- Topological System
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© 2010 Springer-Verlag Berlin Heidelberg
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Queffélec, M. (2010). Dynamical Systems Associated with Sequences. 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_4
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DOI: https://doi.org/10.1007/978-3-642-11212-6_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11211-9
Online ISBN: 978-3-642-11212-6
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