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.
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
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