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Entropy as a function and the variational principle

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

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  • Variational Principle
  • Open Neighborhood
  • Open Cover
  • Topological Entropy
  • Compact Hausdorff Space

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5.4. References

  1. ADLER, R. L., KONHEIM, A. G. and McANDREW, M. H., Topological entropy. Trans. Amer. Math. Soc. 114 (1965), 309–319.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. DINABURG, E. I., The relation between topological entropy and metric entropy. Soviet Math. Doklady 11 (1970), 13–16.

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  3. GOODMAN, T. N. T., Relating topological entropy and measure entropy. Bull. London Math. Soc. 3 (1971), 176–180.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. GOODWYN, L. W., Comparing topological entropy with measure theoretic entropy. Amer. J. of Math. 94 (1972), 366–388.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. BOWEN, R., Entropy for group endomorphisms and homogeneous spaces. Trans. Amer. Math. Soc. 153 (1971), 401–414.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. RUELLE, D., Statistical Mechanics-Rigourous results. Benjamin (1969).

    Google Scholar 

  7. WALTERS, P., A variational principle for the pressure of continuous transformations. Amer. J. of Math. 97 (1975), 937–971.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. MISIUREWICZ, M., A short proof of the variational principle for a Z n+ -action on a compact space. Astérisque no 40 (1977), 147–158.

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  9. JACOBS, K., Ergodic decomposition of the Kolmogorov-Sinaī invariant, in Proc. Internat. Symp. in Ergodic Theory, Academic Press, New-York (1963), 173–190.

    Google Scholar 

  10. MEYER, P. A., Probabilités et potentiel. Hermann (1966).

    Google Scholar 

  11. DENKER, M., GRILLENBERGER, C., SIGMUND, K., Ergodic Theory on compact spaces. Lecture Notes in Mathematics 527. Springer-Verlag, Berlin, Heidelberg, New-York (1976).

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© 1985 Springer-Verlag

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Ollagnier, J.M. (1985). Entropy as a function and the variational principle. In: Ergodic Theory and Statistical Mechanics. Lecture Notes in Mathematics, vol 1115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101580

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  • DOI: https://doi.org/10.1007/BFb0101580

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  • Print ISBN: 978-3-540-15192-0

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