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Regularity of topological and metric entropy of hyperbolic flows

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References

  1. Abramov, L.M.: On the entropy of a flow. Trasl. Am. Math. Soc.49, 167–170 (1966)

    MATH  Google Scholar 

  2. Bowen, R.: Periodic orbits for hyperbolic flows. Am. J. Math.94, 1–30 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bowen, R.: Symbolic dynamics for hyperbolic flows. Am. J. Math.95, 429–459 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bowen, R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms. (Lect. Notes Math., vol. 470) Berlin Heidelberg New York: Springer 1975

    MATH  Google Scholar 

  5. Bowen, R., Ruelle, D.: The Ergodic Theory of Axiom A flows. Invent. Math.29, 181–202 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  6. Dinaburg, E.I.: On the relations among various entropy characteristics of dynamical systems. Math. USSR Izv.5, 337–378 (1971)

    Article  Google Scholar 

  7. Kadison, R.V., Ringrose, J.R.: Fundamentals of the theory of operator algebras, vol. 1. London New York: Academic Press 1983

    MATH  Google Scholar 

  8. Katok, A., Knieper, G., Weiss, H.: Regularity of topological entropy. (to appear)

  9. Katok, A., Knieper, G., Pollicott, M., Weiss, H.: Differentiability and Analyticity of topological entropy for Anosov and Geodesic flows. Invent. Math.98, 581–597 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  10. Knieper, G.: Measure theoretic entropy is twice differentiable at locally symmetric spaces of negative curvature. (unpublished)

  11. Knieper, G., Weiss, H.: Regularity of measure theoretic entropy for geodesic flows of negative curvature. Invent. Math.95, 579–589 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  12. Lang, S.: Analysis II. Reading, MA: Addison-Wesley 1969

    MATH  Google Scholar 

  13. Llave, R. de la, Marco, J., Moriyon, R.: Canonical perturbation theory of Anosov systems and regularity results for Livsic cohomology equation. Ann. Math.123, 537–611 (1986)

    Article  Google Scholar 

  14. Manning, A.: A relation between Lyapunov exponents, Hausdorff dimension and entropy. Ergodic Theory Dyn. Syst.1, 451–459 (1981)

    MATH  MathSciNet  Google Scholar 

  15. Mañé, R.: The Hausdorff dimension of horseshoes of diffeomorphims of surfaces. Bol. Soc. Bras. Mat.20 (No. 2), 1–24 (1990)

    MATH  Google Scholar 

  16. Margulis, G.: Certain measures associated with U-flows on compact manifolds. Funct. Anal. Appl.4 (no. 1), 55–67 (1969)

    Article  MathSciNet  Google Scholar 

  17. Misiurewicz, M.: On non-continuity of topological entropy. Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys.19 (no. 4), 319–320 (1971)

    MATH  MathSciNet  Google Scholar 

  18. Misiurewicz, M.: Diffeomorphisms without any measure with maximal entropy. Bull. Acad. Pol. Sci, Ser. Sci. Astron. Phys.21 (no. 10), 903–910 (1973)

    MATH  MathSciNet  Google Scholar 

  19. Newhouse, S.: Continuity properties of entropy. Ergodic Theory Dyn. Syst. Conley Memorial issue vol.8 *, 283–300 (1988)

    MATH  MathSciNet  Google Scholar 

  20. Ruelle, D.: Thermodynamic Formalism. (Encicl. Math. Appl., vol. 5) Reading, MA: Addison-Wesley 1978

    MATH  Google Scholar 

  21. Shub, M.: Global Stability of Dynamical Systems. Berlin Heidelberg New York: Springer 1987

    MATH  Google Scholar 

  22. Walters, P.: An Introduction to Ergodic theory. (Grad. Texts Math., vol. 79) Berlin Heidelberg New York: Springer 1982

    MATH  Google Scholar 

  23. Yomdim, Y.: Volume growth and entropy. Isr. J. Math.57, 285–300 (1987)

    Google Scholar 

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Research supported by CNPq Brasil

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Contreras, G. Regularity of topological and metric entropy of hyperbolic flows. Math Z 210, 97–111 (1992). https://doi.org/10.1007/BF02571785

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