Inventiones mathematicae

, Volume 112, Issue 1, pp 541–576 | Cite as

Sinai-Bowen-Ruelle measures for certain Hénon maps

  • Michael Benedicks
  • Lai-Sang Young


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  1. [B] Bowen, R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms. (Lect. Notes Math., vol. 470) Berlin Heidelberg New York Springer: 1975Google Scholar
  2. [BC1] Benedicks, M., Carleson, L.: On iterates ofx→1-ax 2 on (-1,1). Ann. Math.122, 1–25 (1985)Google Scholar
  3. [BC2] Benedicks, M., Carleson, L.: The dynamics of the Hénon map. Ann. Math.133, (1991), 73–169Google Scholar
  4. [BM] Benedicks, M. Moeckel, R.: An attractor for the Hénon map. Zürich: ETH (Preprint)Google Scholar
  5. [BY] Benedicks, M., Young, L.S.: Random perturbations and invariant measures for certain one-dimensional maps. Ergodic Theory Dyn. Syst. (to appear)Google Scholar
  6. [L] Ledrappier, F.: Propriétés ergodiques des mesures de Sinai. Publ. Math., Inst. Hautes Etud. Sci.59, 163–188 (1984)Google Scholar
  7. [LS] Ledrappier, F., Strelcyn, J.-M.: A proof of the estimation from below in Pesin's entropy formula. Ergodic Theory Dyn. Sys2 203–219 (1982)Google Scholar
  8. [LY] Ledrappier, F., Young, L.-S.: The metric entropy of diffemorphisms. Part I. Characterization of measures satisfying Pesin's formula. Part II. Relations between entropy, exponents and dimension. Ann. Math.122, 509–539, 540–574 (1985)Google Scholar
  9. [MV] Mora, L., Viana, M.: Abundance of strange attractors. IMPA reprint (1991)Google Scholar
  10. [K] Katok, A.: Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Publ. Math., Inst. Hautes Étud. Sci.51, 137–174 (1980)Google Scholar
  11. [P1] Pesin, Ja.G.: Families of invariant manifolds corresponding to non-zero characteristic exponents. Math. USSR, Izv.10, 1261–1305 (1978)Google Scholar
  12. [P2] Pesin, Ja.G.: Characteristic Lyaponov exponents and smooth ergodic theory. Russ. Math. Surv.32.4, 55–114 (1977)Google Scholar
  13. [PS] Pugh, C., Shub, M.: Ergodic Attractors. Trans. Am. Math. Soc.312, 1–54 (1989)Google Scholar
  14. [Ro] Rohlin, V.A.: On the fundamental ideas of measure theory. Transl., Am. Math. Soc.10, 1–52 (1962)Google Scholar
  15. [Ru1] Ruelle, D.: A measure associated with Axiom A attractors. Am. J. Math.98, 619–654 (1976)Google Scholar
  16. [Ru2] Ruelle, D.: Ergodic theory of differentialble dynamical systems. Publ. Math., Inst. Hautes Étud. Sci.50, 27–58 (1979)Google Scholar
  17. [S1] Sinai, Ya. G.: Markov partitions andC-diffeomorphisms. Func. Anal. Appl.2, 64–89 (1968)Google Scholar
  18. [S2] Sinai, Ya. G.: Gibbs measures in ergodic theory. Russ. Math. Surv.27:4, 21–69 (1972)Google Scholar
  19. [Y1] Young, L.-S.: Dimension, entropy and Lyapunov exponents. Ergodic Theory Dyn. Syst.2, 163–188 (1982)Google Scholar
  20. [Y2] Young, L.-S.: A Bowen-Ruelle measure for certain piecewise hyperbolic maps. Trans. Am. Math. Soc.287, 41–48 (1985)Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Michael Benedicks
    • 1
  • Lai-Sang Young
    • 2
  1. 1.Department of MathematicsRoyal Institute of TechnologyStockholmSweden
  2. 2.Department of MathematicsUCLALos AngelesUSA

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