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Entropy of abstract dynamical systems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1115)

Keywords

  • Conditional Expectation
  • Probability Vector
  • Amenable Group
  • Conditional Entropy
  • Finite Part

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4.5. References

  1. BILLINGSLEY, P., Ergodic Theory and Information. Wiley series in probability and mathematical statistics (1965).

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  2. KOLMOGOROV, A. N., A new invariant for transitive dynamical systems. Doklady Akad. Nauk SSSR 119 (1958), 861–864.

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  3. SINAT, Y. G., On the notion of entropy of a dynamical system. Doklady Akad. Nauk SSSR 124 (1959), 768–771.

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  4. ROKHLIN, V. A., Lectures on the entropy theory of measure-preserving transformations. Russian Math. Surveys 22 (1967), 1–52.

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  5. PARRY, W., Entropy and generators in Ergodic Theory. Benjamin (1969).

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  6. ORNSTEIN, D. S., Bernoulli shifts with the same entropy are isomorphic. Adv. in Math. 4 (1970), 337–352.

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  7. ORNSTEIN, D. S., Ergodic theory, Randomness and dynamical systems. Yale mathematical monographs. Yale University press (1974).

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  8. SMORODINSKY, M., On Ornstein’s isomorphism theorem for Bernoulli-shifts. Adv. in Math. 9 (1972), 1–9.

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  9. KIEFFER, J. C., A generalized Shannon-McMillan theorem for the action of an amenable group on a probability space. The Annals of Proba. 3 (1975), 1031–1037.

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© 1985 Springer-Verlag

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Ollagnier, J.M. (1985). Entropy of abstract dynamical systems. In: Ergodic Theory and Statistical Mechanics. Lecture Notes in Mathematics, vol 1115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101579

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  • DOI: https://doi.org/10.1007/BFb0101579

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15192-0

  • Online ISBN: 978-3-540-39289-7

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