Hausdorff dimension of quasi-circles

  • Rufus Bowen


HAUSDORFF Dimension Surface Group Gibbs Measure Jordan Curve Kleinian Group 
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  1. [1]
    A. Akaza, Local property of the singular sets of some Kleinian groups,Tohoku Math. J.,25 (1973), 1–22.Google Scholar
  2. [2]
    A. F. Beardon, The Hausdorff dimension of singular sets of properly discontinuous groups,Amer. J. Math.,88 (1966), 722–736.zbMATHCrossRefGoogle Scholar
  3. [3]
    ——, The exponent of convergence of Poincaré series,Proc. London Math. Soc. (3),18 (1968), 461–483.zbMATHCrossRefGoogle Scholar
  4. [4]
    L. Bers, Uniformization by Beltrami equations,Comm. Pure Appl. Math.,14 (1961), 215–228.zbMATHCrossRefGoogle Scholar
  5. [5]
    ——, Uniformization, moduli and Kleinian groups,Bull. London Math. Soc.,4 (1972), 257–300.zbMATHCrossRefGoogle Scholar
  6. [6]
    ——, On Hilbert’s 22nd problem,Proc. Symp. Pure Math.,28 (1976), 559–609.Google Scholar
  7. [7]
    R. Bowen, Equilibrium states and the ergodic theory of Anosov diffeomorphisms,Springer Lecture Notes in Math.,470 (1975).Google Scholar
  8. [8]
    V. Chuckrow, On Schottky groups with applications to Kleinian groups,Ann. of Math.,88 (1968), 47–61.CrossRefGoogle Scholar
  9. [9]
    G. A. Hedlund, On the metrical transitivity of the geodesics on closed surfaces of constant negative curvature,Annals of Math.,35 (1934), 787–808.CrossRefGoogle Scholar
  10. [10]
    A. N. Livshits, Homology properties of Y-systems,Math. Notes Acad. Sci. USSR,19 (1971), 758–763.CrossRefGoogle Scholar
  11. [11]
    A. Marden, Isomorphisms between Fuchsian groups, inAdvances in Complex Function Theory, Lecture Notes in Math.,505, Springer Verlag, 1976 (Kirwan & Zalcman Ed.).Google Scholar
  12. [12]
    M. Morse,Symbolic dynamics (lecture notes), Institute for Advanced Study, Princeton.Google Scholar
  13. [13]
    G. D. Mostow,Strong rigidity of locally symmetric spaces, Princeton Univ. Press, 1973, p. 178. Also: Rigidity of real hyperbolic space forms,Publ. math. IHES, vol.34 (1968), 53–104.Google Scholar
  14. [14]
    J. Nielsen, Undersuchungen zur Topologie der geschlossenen zweiseitigen Flächen,Acta Math.,50 (1927), 189–358.CrossRefGoogle Scholar
  15. [15]
    S. J. Patterson, The limit set of a Fuchsian group,Acta. Math.,136 (1976), 241–273.zbMATHCrossRefGoogle Scholar
  16. [16]
    D. Ruelle, Statistical mechanics of a one-dimensional lattice gas,Comm. Math. Phys.,9 (1968), 267–278.zbMATHCrossRefGoogle Scholar
  17. [17]
    ——, Zeta-functions for expanding maps and Anosov flows,Inventiones Math.,34 (1975), 231–242.CrossRefGoogle Scholar
  18. [18]
    C. L. Siegel,Topics in complex function theory, vol. 2, Wiley-Interscience, 1971.Google Scholar
  19. [19]
    Ya. G. Sinai, Gibbs measures in ergodic theory,Russ. Math. Surveys, no. 4 (166), 1972, 21–64.Google Scholar
  20. [20]
    W. Veech,A second course in complex analysis, Benjamin, 1967.Google Scholar
  21. [21]
    A. Zygmund,Trigonometric series, vol. 1, Cambridge, 1968.Google Scholar
  22. [22]
    W. Thurston,Geometry and Topology of 3-manifolds, section 5·9, mimeographed notes, Princeton Univ., 1978.Google Scholar

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© Publications mathématiques de l’I.H.É.S 1979

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  • Rufus Bowen

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