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Polynomial diffeomorphisms ofC 2

III. Ergodicity, exponents and entropy of the equilibrium measure

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References

  1. Bedford, E., Smillie, J.: Polynomial diffeomorphisms of C2: Currents, equilibrium measure and hyperbolicity. Invent. Math.87 (1990)

  2. Bedford, E., Smillie, J.: Fatou-Bieberbach domains arising from polynomial automorphisms. Indiana Univ. Math. J.40, 789–792 (1991)

    Article  Google Scholar 

  3. Bedford, E., Smillie, J.: Polynomial diffeomorphisms of C2. II. Stable manifolds and recurrence. J. Am. Math. Soc.4, 657–679 (1991)

    Google Scholar 

  4. Bedford, E., Taylor, B.A.: Fine topology, Šilov boundary and (dd c)n, J. Funct. Anal.72, 225–251 (1987)

    Article  Google Scholar 

  5. Brolin, H.: Invariant sets under iteration of rational functions. Ark. Mat.6, 103–144 (1965)

    Google Scholar 

  6. Carleson, L.: Complex dynamics. U.C.L.A. course notes 1990

  7. Fathi, A., Herman, M., Yoccoz, J.-C.: A proof of Pesin's stable manifold theorem. In: Geometric dynamics. J. Palis (ed.). (Lect. Notes Math. vol. 1007, pp. 177–215) Berlin Heidelberg New York: Springer 1983

    Google Scholar 

  8. Fornaess, J.-E., Sibony, N.: Complex Hénon mappings in C2 and Fatou Bieberbach domains. Duke Math. J.65, 345–380 (1992)

    Article  Google Scholar 

  9. Freire, A., Lopes, A., Mañé, R.: An invariant measure for rational maps. Bol. Soc. Bras. Mat.6, 45–62 (1983)

    Google Scholar 

  10. Friedland, S., Milnor, J.: Dynamical properties of plane polynomial automophisms. Ergodic Theory Dyn. Syst.9, 67–99 (1989)

    Google Scholar 

  11. Hubbard, J.: personal communication

  12. Hubbard, J.H., Oberste-Vorth, R.: Hénon mappings in the complex domain. preprint

  13. Katok, A.: Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Publ. Math. Inst. Hautes Etud. Sci.51, 137–174 (1980)

    Google Scholar 

  14. Ledrappier, F., Strelcyn, J.-M.: A proof of the estimation from below in Pesin's entropy formula. Ergodic Theory Dyn. Syst.2, 203–219 (1982)

    Google Scholar 

  15. Lelong, P.: Fonctions plurisousharmoniques d'ordre fini dans Cn. J. Anal. Math.12, 365–407 (1964)

    Google Scholar 

  16. Ljubich, M.Ju.: Entropy properties of rational endomorphisms of the Reimann sphere. Ergodic Theory Dyn. Syst.3, 351–385 (1983)

    Google Scholar 

  17. Manning, A.: The dimension of the maximal measure for a polynomial map. Ann. Math.119, 425–430 (1984)

    Google Scholar 

  18. Newhouse, S.: Lectures on dynamical systems, in Dynamical Systems, C.I.M.E. Lectures Bressanone, Italy, 1978. Progress in Mathematics 8. Basel Boston Stuttgart: Birkhäuser 1980

    Google Scholar 

  19. Przytycki, F.: Riemann map and holomorphic dynamics. Invent. Math.85, 439–455 (1986)

    Article  Google Scholar 

  20. Ruelle, D.: Ergodic theory of differentiable dynamical systems. Publ. Math. Inst. Hautes Etud. Sci.50, 275–306 (1979)

    Google Scholar 

  21. Skoda, H.: Sous ensembles analytiques d'ordre fini ou infini dans Cn. Bull. Soc. Math. Fr.100, 353–408 (1972)

    Google Scholar 

  22. Sibony, N.: Iteration of polynomials U.C.L.A. lecture notes

  23. Smillie, J.: The entropy of polynomial diffeomorphisms of C2, Ergodic Theory Dyn. Syst.10, 823–827 (1990)

    Google Scholar 

  24. Tortrat, P.: Aspects potentialistes de l'itération des polynômes. Séminaire de Théorie du Potential, Paris, No. 8 (Lect. Notes Math., vol. 1235) Berlin Heidelberg New York: Springer 1987

    Google Scholar 

  25. Tsuji, M.: Potential theory, New York: Chelsea 1975

    Google Scholar 

  26. Walters, P.: An introduction to ergodic theory. Berlin Heidelberg New York: Springer 1982

    Google Scholar 

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

    Google Scholar 

  28. Young, L.-S.: Dimension, entropy and Lyapunov exponents, Ergodic Theory Dyn. Syst.2, 109–124 (1982)

    Google Scholar 

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Partially supported by NSF grant #DMS-8602020

Partially supported by NSF grant #DMS-9003101 and MSI of Cornell University

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Bedford, E., Smillie, J. Polynomial diffeomorphisms ofC 2 . Math. Ann. 294, 395–420 (1992). https://doi.org/10.1007/BF01934331

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