Advertisement

Problems of Information Transmission

, Volume 48, Issue 1, pp 11–20 | Cite as

Boundary distortion rate in synchronized systems: Geometrical meaning of entropy

  • S. A. KomechEmail author
Information Theory

Abstract

The geometrical meaning of the Kolmogorov entropy is studied. The relation between the entropy and boundary distortion rate in the phase space is obtained for a wide class of symbolic dynamical systems, namely synchronized systems.

Keywords

Information Transmission Geometrical Meaning Markov Shift Synchronize System Shift Transformation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gurevich, B.M., Geometric Interpretation of Entropy for Random Processes, Sinai’s Moscow Seminar on Dynamical Systems, Bunimovich, L.A., Gurevich, B.M., and Pesin, Ya.B., Eds., Providence, R.I.: Amer. Math. Soc., 1996, pp. 81–87.Google Scholar
  2. 2.
    Zaslavsky, G.M., Chaos in dynamic systems, New-York: Harwood Academic Publishers, 1985.Google Scholar
  3. 3.
    Blanchard, F. and Hansel, G., Systémes codés, Theoret. Comput. Sci., 1986, vol. 44, no. 1, pp. 17–49.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Weiss, B., Subshifts of Finite Type and Sofic Systems, Monatsh. Math., 1973, vol. 77, no. 5, pp. 462–474.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Entropy of Hidden Markov Processes and Connections to Dynamical Systems (Papers from the Banff Int. Research Station Workshop), Marcus, B., Petersen, K., and Weissman, T., Eds., Cambridge: Cambridge Univ. Press, 2011.Google Scholar
  6. 6.
    Billingsley, P., Ergodic Theory and Information, New York: Wiley, 1965. Translated under the title Ergodicheskaya teoriya i informatsiya, Moscow: Mir, 1969.zbMATHGoogle Scholar
  7. 7.
    Bellow, A., Jones, R., and Rosenblatt, J., Convergence of Moving Averages, Ergodic Theory Dynam. Systems, 1990, vol. 10, no. 1, pp. 43–62.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Kharkevich Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia

Personalised recommendations