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Substitutions and symbolic dynamical systems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1794)

Abstract

The aim of this chapter is to introduce the fundamental notions of ergodic theory, through the study of a few examples of symbolic dynamical systems.

To improve lisibility, some of the definitions and propositions stated in Chap. 1 are repeated in the present chapter.

In the course of this chapter, we shall use at some points notions of measure theory and spectral theory; when there is no explanation in the text, the reader is referred to any standard book, such as [122] and [340]; however, we have tried to isolate these places, and the reader can skip them without damage to his general understanding.

Keywords

  • Ergodic Theorem
  • Spectral Type
  • Invariant Probability Measure
  • Fibonacci Sequence
  • Unique Ergodicity

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This chapter has been written by S. Ferenczi

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© 2002 Springer-Verlag Berlin Heidelberg

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(2002). Substitutions and symbolic dynamical systems. In: Fogg, N.P., Berthé, V., Ferenczi, S., Mauduit, C., Siegel, A. (eds) Substitutions in Dynamics, Arithmetics and Combinatorics. Lecture Notes in Mathematics, vol 1794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45714-3_5

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  • DOI: https://doi.org/10.1007/3-540-45714-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44141-0

  • Online ISBN: 978-3-540-45714-5

  • eBook Packages: Springer Book Archive