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Discrete conformal groups and measurable dynamics. (English) Zbl 0489.58027

MSC:
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
28D05 Measure-preserving transformations
54F45 Dimension theory in general topology
30F15 Harmonic functions on Riemann surfaces
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
54H20 Topological dynamics (MSC2010)
53C30 Differential geometry of homogeneous manifolds
53C22 Geodesics in global differential geometry
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References:
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[2] Lars V. Ahlfors, Kleinian groups, Scripta Math. 27 (1964), 97 – 103 (1964). · Zbl 0132.30704
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[4] Jon Aaronson, On the pointwise ergodic behaviour of transformations preserving infinite measures, Israel J. Math. 32 (1979), no. 1, 67 – 82. · Zbl 0462.28015 · doi:10.1007/BF02761186 · doi.org
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[10] Wolfgang Krieger, On ergodic flows and the isomorphism of factors, Math. Ann. 223 (1976), no. 1, 19 – 70. · Zbl 0332.46045 · doi:10.1007/BF01360278 · doi.org
[11] William LeVeque, Continued fractions for the Gaussian field, Indag. Math. (1952). · Zbl 0048.27902
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[14] Dennis Sullivan, Disjoint spheres, approximation by imaginary quadratic numbers, and the logarithm law for geodesics, Acta Math. 149 (1982), no. 3-4, 215 – 237. · Zbl 0517.58028 · doi:10.1007/BF02392354 · doi.org
[15] Dennis Sullivan, On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook Conference (State Univ. New York, Stony Brook, N.Y., 1978) Ann. of Math. Stud., vol. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 465 – 496.
[16] Dennis Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math. 50 (1979), 171 – 202. · Zbl 0439.30034
[17] Dennis Sullivan, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. 153 (1984), no. 3-4, 259 – 277. · Zbl 0566.58022 · doi:10.1007/BF02392379 · doi.org
[18] Dennis Sullivan, Growth of positive harmonic functions and Kleinian group limit sets of zero planar measure and Hausdorff dimension two, Geometry Symposium, Utrecht 1980 (Utrecht, 1980) Lecture Notes in Math., vol. 894, Springer, Berlin-New York, 1981, pp. 127 – 144.
[19] Klaus Schmidt, Cocycles of ergodic group actions, Warwick Notes, 1976.
[20] Bill Thurston, (i) Geometry and topology of three-manifolds, preprint, Princeton Univ., 1978; to be published by Princeton Univ. Press, 1982.
[21] Pekka Tukia, Rigidity of Kleinian groups and dimensionality of the limit set, preprint, Univ. of Helsinki, 1981. · Zbl 0431.30011
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