Invariant measures of the geodesic flow and measures at infinity on negatively curved manifolds

 Access to full text

 Full (PDF)

1. [A1] A. Ancona, Negatively Curved Manifolds, Elliptic Operators, and the Martin Boundary, Ann. Math., Vol. 125, 1987, pp. 495-536. Zbl0652.31008MR890161
2. [A2] A. Ancona, Positive Harmonic Functions and Hyperbolicity, Springer, Lect. Notes Math., Vol. 1344, 1988, pp. 1-23. Zbl0677.31006MR973878
3. [A3] A. Ancona, Sur les fonctions propres des variétés de Cartan-Hadamard, Comm. Math. Helvetici, Vol. 64, 1989, pp. 62-83. Zbl0689.53027MR982562
4. [Al] A.D. Aleksandrov, A Theorem on Triangles in a Metric Space and Some of Its Applications, Trudy Steklov Mat. Inst., Vol. 38, 1951, pp. 5-23 (in Russian). Zbl0049.39501MR49584
5. [AS] M.T. Anderson and R. Schoen, Positive Harmonic Functions on Complete Manifolds of Negative Curvature, Ann. Math., Vol. 121, 1985, pp. 429-461. Zbl0587.53045MR794369
6. [B1] R. Bowen, Periodic Orbits for Hyperbolic Flows, Am. J. Math., Vol. 94, 1972, pp. 1-30. Zbl0254.58005MR298700
7. [B2] R. Bowen, Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Springer, Lect. Notes Math., Vol. 470, 1975. Zbl0308.28010MR442989
8. [BGS] W. Ballmann, M. Gromov and V. Schroeder, Manifolds of Nonpositive Curvature, Birkhäuser, Basel, 1985. Zbl0591.53001MR823981
9. [BK] M. Brin and A. Katok, On Local Entropy, Springer, Lect. Notes Math., Vol. 1007, 1983, pp. 30-38. Zbl0533.58020MR730261
10. [BR] R. Bowen and D. Ruelle, The Ergodic Theory of Axiom A Flows, Invent. Math., Vol. 29, 1975, pp. 181-202. Zbl0311.58010MR380889
11. [Bu] D. Ju. Burago, A New Approach to the Computation of the Entropy of a Geodesic Flow and Similar Dynamical Systems, Soviet Math. Dokl., Vol. 37, 1988, pp. 501-504. Zbl0706.58050MR947227
12. [C] I. Chavel, Eigenvalues in Riemannian Geometry, Academic Press, Orlando, 1984. Zbl0551.53001MR768584
13. [CDP] M. Coornaert, T. Delzant, A. Papadopoulos, Notes sur les groupes hyperboliques de Gromov, Publ. I.R.M.A., Strasbourg, 1989. 
14. [CE] J. Cheeger and D.G. Ebin, Comparison Theorems in Riemannian Geometry, North Holland, Amsterdam, 1975. Zbl0309.53035MR458335
15. [D] E.B. Dynkin, Markov processes and related problems of analysis, London Math. Soc. Lect. Note Ser., Vol. 54, 1982. Zbl0498.60067MR678918
16. [E] K.D. Elworthy, Stochastic differential equations on manifolds, London Math. Soc. Lect. Note Ser., Vol. 70, 1982. Zbl0514.58001MR675100
17. [EO'N] P. Eberlein and B. O'Neill, Visibility manifolds, Pac. J. Math., Vol. 46, 1973, pp. 45-109. Zbl0264.53026MR336648
18. [G] M. Gromov, Hyperbolic groups, M.S.R.I. Publ., Vol. 8, 1987, pp. 75-263. Zbl0634.20015MR919829
19. [GH] E. Ghys, P. De La Harpe éd., Sur les groupes hyperboliques d'après Mikhael Gromov, Birkhäuser, Basel, 1990. Zbl0731.20025MR1086648
20. [H1] U. Hamenstadt, A New Description of the Bowen-Margulis measure, Erg. Th. Dynam. Sys., Vol. 9, 1989, pp. 455-464. Zbl0722.58029MR1016663
21. [H2] U. Hamenstadt, Time Preserving Conjugacies of Geodesic Flows, preprint. Zbl0766.58045MR1162399
22. [H3] U. Hamenstadt, An Explicite Description of Harmonic Measure, preprint. MR1076134
23. [IW] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North Holland/Kodansha, Amsterdam, 1981. Zbl0495.60005MR637061
24. [K] V.A. Kaimanovich, Brownian Motion and Harmonic Functions on Covering Manifolds. An Entropy Approach, Soviet Math. Dokl., Vol. 33, 1986, pp. 812- 816. Zbl0615.60074MR852647
25. [Ki] Y. Kifer, A Lower Bound for Haudorff Dimension of Harmonic Measures on Negatively Curved Manifolds, preprint. MR1088826
26. [KL] Y. Kifer and F. Ledrappier, Hausdorff Dimension of Harmonic Measures on Negatively Curved Manifolds, preprint. Zbl0702.58080MR951889
27. [Ko1] T. Kori, Problème de Neumann sur les espaces harmoniques, Math. Ann., Vol. 224, 1976, pp. 53-76. Zbl0346.31006MR435428
28. [Ko2] T. Kori, La théorie des espaces fonctionnelles a nullité 1 et le problème de Neumann sur les espaces harmonique, Ann. Inst. Fourier Grenoble, Vol. 27, 1977, pp. 45-119. Zbl0357.31008MR508016
29. [KV] V.A. Kaimanovich and A.M. Vershik, Random Walks on Discrete Groups: Boundary and Entropy, Ann. Prob., Vol. 11, 1983, pp. 457-490. Zbl0641.60009MR704539
30. [L1] F. Ledrappier, Une relation entre entropie, dimension et exposant pour certaines marches aléatoires, C.R. Acad. Sci. Paris, T. 296, Série I, 1983, pp. 369-372. Zbl0529.60071MR699165
31. [L2] F. Ledrappier, Ergodic properties of Brownian motion on covers of compact negatively curved manifolds, Bol. Soc. Bras. Mat., Vol. 19, 1988, pp. 115-140. Zbl0685.58036MR1018929
32. [L3] F. Ledrappier, Harmonic measures and Bowen-Margulis measures, preprint. Zbl0728.53029MR1088820
33. [LY] F. Ledrappier and L.-S. Young, The Metric Entropy of Diffeomorphisms I, II, Ann. Math., Vol. 122, 1985, pp. 509-574. Zbl0605.58028MR819556
34. [M1] G.A. Margulis, Applications of Ergodic Theory to the Investigation of Manifolds of Negative Curvature, Funct. Anal. Appl., Vol. 3, 1969, pp. 335-336. Zbl0207.20305MR257933
35. [M2] G.A. Margulis, Certain Measures Associated with U-Flows on Compact Manifolds, Funct. Anal. Appl., Vol. 4, 1970, pp. 55-67. Zbl0245.58003MR272984
36. [Man] A. Manning, Topological Entropy for Geodesic Flows, Ann. Math., Vol. 110, 1979, pp. 567-573. Zbl0426.58016MR554385
37. [O] J.-P. Otal, Sur la géométrie symplectique de l'espace des géodésiques d'une variété à courbure négative, preprint. Zbl0777.53042
38. [P1] S.J. Patterson, The Limit Set of a Fuchsian Group, Acta Math., Vol. 136, 1976, pp. 241-243. Zbl0336.30005MR450547
39. [P2] S.J. Patterson, Lectures on Measures on Limit Sets of Kleinian Groups, London Math. Soc. Lect. Note Ser., Vol. 111, 1987, pp. 281-323. Zbl0611.30036MR903855
40. [Pe] Ya B. Pesin, Geodesic Flows with Hyperbolic Behaviour of the Trajectories and Objects Connected with Them, Russian Math. Surveys, Vol. 36, 4, 1981, pp. 1-59. Zbl0493.58001MR629682
41. [Pr] J.-J. Prat, Etude asymptotique et convergence angulaire du mouvement Brownien sur une variété à courbure négative, C.R. Acad. Sci. Paris, T. 280, Series A, 1975, pp. 1539-1542. Zbl0309.60052MR388557
42. [S1] D. Sullivan, Cycles for the Dynamical Study of Foliated Manifolds and Complex Manifolds, Invent. Math., Vol. 36, 1976, pp. 225-255. Zbl0335.57015MR433464
43. [S2] D. Sullivan, The Density at Infinity of a Discrete Group of Hyperbolic Motions, Publ. Math. I.H.E.S., Vol. 50, 1979, pp. 171-202. Zbl0439.30034MR556586
44. [Si] Ya G. Sinai, Gibbs Measures in Ergodic Theory, Russian Math. Surveys, Vol. 27, 4, 1972, pp. 21-69. Zbl0246.28008MR399421
45. [Ya] S.-T. Yau, Harmonic Functions on Complete Riemannian Manifolds, Comm. Pure Appl. Math., Vol. 28, 1975, pp. 201-228. Zbl0291.31002MR431040
46. [Yo] L.-S. Young, Dimension, Entropy and Lyapunov Exponents, Erg. Th. Dynam. Sys., Vol. 2, 1982, pp. 109-129. Zbl0523.58024MR684248

1. Ursula Hamenstädt, Some aspects of the Laplace operator in negative curvature
2. Thomas Roblin, Sur la fonction orbitale des groupes discrets en courbure négative
3. Nathanaël Enriquez, Jacques Franchi, Masse des pointes, temps de retour et enroulements en courbure négative
4. Barbara Schapira, Lemme de l'ombre et non divergence des horosphères d'une variété géométriquement finie
5. François Ledrappier, Structure au bord des variétés à courbure négative
6. Vadim A. Kaimanovich, Howard Masur, The Poisson Boundary of the Mapping Class Group and of Teichmüller Space
7. Sébastien Blachère, Peter Haïssinsky, Pierre Mathieu, Harmonic measures versus quasiconformal measures for hyperbolic groups
8. Martine Babillot, Marc Peigné, Asymptotic laws for geodesic homology on hyperbolic manifolds with cusps