Advertisement

An Introduction to Ergodic Theory

Chapter
Part of the Mathematics for Industry book series (MFI, volume 5)

Abstract

Ergodic theory concerns with the study of the long-time behavior of a dynamical system. An interesting result known as Birkhoff’s ergodic theorem states that under certain conditions, the time average exists and is equal to the space average. The applications of ergodic theory are the main concern of this note. We will introduce fundamental concepts in ergodic theory, Birkhoff’s ergodic theorem and its consequences.

Keywords

Benford’s law Ergodic theorem Markov chain Measure-preserving transformation Poincaré’s recurrence theorem Strong-mixing Weak-mixing 

References

  1. 1.
    R. Durrett, Probability: Theory and Examples, 4th edn. (Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2010)Google Scholar
  2. 2.
    L. Kuipers, H. Niederreiter, Uniform Distribution of Sequences. (Dover Publishing, New York, 2006)Google Scholar
  3. 3.
    J.R. Norris, Markov Chains. (Cambridge University Press, Cambridge, 1997)Google Scholar
  4. 4.
    P. Walters, An Introduction to Ergodic Theory. Graduate Texts in Mathematics, vol. 79. (Springer, New York, 1982)Google Scholar

Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of Mathematics for IndustryKyushu UniversityNishiku, FukuokaJapan

Personalised recommendations