Discrete conformal groups and measurable dynamics
Author:
Dennis Sullivan
Journal:
Bull. Amer. Math. Soc. 6 (1982), 5773
MSC (1980):
Primary 32H20, 58F11, 58F17; Secondary 58F18, 10F05
MathSciNet review:
634434
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References 
Similar Articles 
Additional Information

Lars
V. Ahlfors, Finitely generated Kleinian groups, Amer. J. Math.
86 (1964), 413–429. MR 0167618
(29 #4890)

Lars
V. Ahlfors, Kleinian groups, Scripta Math. 27
(1964), 97–103 (1964). MR 0171007
(30 #1240)

Lars
V. Ahlfors, Möbius transformations in several dimensions,
Ordway Professorship Lectures in Mathematics, University of Minnesota,
School of Mathematics, Minneapolis, Minn., 1981. MR 725161
(84m:30028)

Jon
Aaronson, On the pointwise ergodic behaviour of transformations
preserving infinite measures, Israel J. Math. 32
(1979), no. 1, 67–82. MR 531602
(80i:28032), http://dx.doi.org/10.1007/BF02761186

[As] Jon Aaronson and Dennis Sullivan, Rational ergodicity of the geodesic flow on infinite volume hyperbolic manifolds (manuscript).

Lipman
Bers, Spaces of Kleinian groups, Several Complex Variables, I
(Proc. Conf., Univ. of Maryland, College Park, Md., 1970) Springer,
Berlin, 1970, pp. 9–34. MR 0271333
(42 #6216)

Lipmann Bers, (ii) See also these proceedings.

[B] Rufus Bowen, Hausdorff dimension of quasicircles, Inst. Hautes Études Sci. Publ. Math.

[C et al] Alain Connes, Jack Feldman and Benjamin Weiss, Amenable equivalence relations are hyperfinite, Inst. Hautes Études Sci. Publ. Math. preprint, 1980.

[G] Lucy Garnett, Functions and measures harmonic along the leaves of a foliation, Ph.D. Thesis, Dartmouth College, 1981; Inst. Hautes Études Sci. Publ. Math. preprint, June 1980.

Wolfgang
Krieger, On ergodic flows and the isomorphism of factors,
Math. Ann. 223 (1976), no. 1, 19–70. MR 0415341
(54 #3430)

[L] William LeVeque, Continued fractions for the Gaussian field, Indag. Math. (1952).

S.
J. Patterson, The limit set of a Fuchsian group, Acta Math.
136 (1976), no. 34, 241–273. MR 0450547
(56 #8841)

Marina
Ratner, Rigidity of horocycle flows, Ann. of Math. (2)
115 (1982), no. 3, 597–614. MR 657240
(84e:58062), http://dx.doi.org/10.2307/2007014

Dennis
Sullivan, Disjoint spheres, approximation by imaginary quadratic
numbers, and the logarithm law for geodesics, Acta Math.
149 (1982), no. 34, 215–237. MR 688349
(84j:58097), http://dx.doi.org/10.1007/BF02392354

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. MR 624833
(83f:58052)

Dennis
Sullivan, The density at infinity of a discrete group of hyperbolic
motions, Inst. Hautes Études Sci. Publ. Math.
50 (1979), 171–202. MR 556586
(81b:58031)

Dennis
Sullivan, Entropy, Hausdorff measures old and new, and limit sets
of geometrically finite Kleinian groups, Acta Math.
153 (1984), no. 34, 259–277. MR 766265
(86c:58093), http://dx.doi.org/10.1007/BF02392379

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, BerlinNew York, 1981, pp. 127–144. MR 655423
(83h:53054)

Dennis Sullivan, (vi) On the finiteness of cusps, Acta Math. (to appear).

Dennis Sullivan, (vii) The exponential size of a Riemannian manifold relative to heat flow, Acta Math. (submitted).

[Sc] Klaus Schmidt, Cocycles of ergodic group actions, Warwick Notes, 1976.

[T] Bill Thurston, (i) Geometry and topology of threemanifolds, preprint, Princeton Univ., 1978; to be published by Princeton Univ. Press, 1982.

Bill Thurston, (ii) Hyperbolic structures on 3manifolds, I. Deformation of acylindrical manifolds, Ann. of Math. (to appear).

[Tu] Pekka Tukia, Rigidity of Kleinian groups and dimensionality of the limit set, preprint, Univ. of Helsinki, 1981.
 [A] Lars Ahlfors, (i) Finitely generated Kleinian groups, Amer. J. Math. 86 (1964), 413429. MR 167618
 Lars Ahlfors, (ii) Some remarks on Kleinian groups, Tulane Conf. Conformal mappings (1965). MR 171007
 Lars Ahlfors, (iii) Moebius transformations in several dimensions, Minnesota Book Center, Minneapolis, Minn., 1981. MR 725161
 [Aa] Jon Aaronson, Pointwise behaviour of infinite measure preserving transformations, Israel J. Math. Math. 32 (1979). MR 531602
 [As] Jon Aaronson and Dennis Sullivan, Rational ergodicity of the geodesic flow on infinite volume hyperbolic manifolds (manuscript).
 [B] Lipmann Bers, (i) Spaces of Kleinian groups, Several Complex Variables, I, (Maryland, 1970). MR 271333
 Lipmann Bers, (ii) See also these proceedings.
 [B] Rufus Bowen, Hausdorff dimension of quasicircles, Inst. Hautes Études Sci. Publ. Math.
 [C et al] Alain Connes, Jack Feldman and Benjamin Weiss, Amenable equivalence relations are hyperfinite, Inst. Hautes Études Sci. Publ. Math. preprint, 1980.
 [G] Lucy Garnett, Functions and measures harmonic along the leaves of a foliation, Ph.D. Thesis, Dartmouth College, 1981; Inst. Hautes Études Sci. Publ. Math. preprint, June 1980.
 [K] Wolfgang Krieger, On ergodic flows and isomorphisms of factors, Math. Ann. 223 (1976), 1970. MR 415341
 [L] William LeVeque, Continued fractions for the Gaussian field, Indag. Math. (1952).
 [P] S. J. Patterson, The limit set of a Fuchsian group, Acta Math. B6 (1976), 241273. [R] Dan Rudolph, manuscript (Maryland). MR 450547
 [Rn] Marina Ratner, Rigidity of the horocycle flow, preprint, Berkeley, 1980. MR 657240
 [S] Dennis Sullivan, (i) Disjoint spheres, approximation by imaginary quadratic numbers and the logarithm law for geodesics, Acta Math. (to appear). MR 688349
 Dennis Sullivan, (ii) On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, Ann. of Math. Studies, No. 97, Princeton Univ. Press, Princeton, N.J., 1981, pp. 465496. MR 624833
 Dennis Sullivan, (iii) The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math. 50 (1979). MR 556586
 Dennis Sullivan, (iv) Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math. (to appear). MR 766265
 Dennis Sullivan, (v) Growth of positive harmonic functions and Kleinian group limit sets of planar measure zero and Hausdorff dimension two, N. Kuiper 60th Birthday Volume (Holland), SpringerVerlag, 1981. MR 655423
 Dennis Sullivan, (vi) On the finiteness of cusps, Acta Math. (to appear).
 Dennis Sullivan, (vii) The exponential size of a Riemannian manifold relative to heat flow, Acta Math. (submitted).
 [Sc] Klaus Schmidt, Cocycles of ergodic group actions, Warwick Notes, 1976.
 [T] Bill Thurston, (i) Geometry and topology of threemanifolds, preprint, Princeton Univ., 1978; to be published by Princeton Univ. Press, 1982.
 Bill Thurston, (ii) Hyperbolic structures on 3manifolds, I. Deformation of acylindrical manifolds, Ann. of Math. (to appear).
 [Tu] Pekka Tukia, Rigidity of Kleinian groups and dimensionality of the limit set, preprint, Univ. of Helsinki, 1981.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S027309791982149667
PII:
S 02730979(1982)149667
