Differentiability, rigidity and Godbillon-Vey classes for Anosov flows

 Access to full text

 Full (PDF)

1. [1] D. V. ANOSOV, Tangent fields of transversal foliations in U-systems, Math. Notes Acad. Sci., USSR, 2 (5) (1967), 818-823. Zbl0171.42201MR39 #3523
2. [2] D. V. ANOSOV, Geodesic Flows on Closed Riemannian Manifolds with Negative Curvature, Proc. Steklov Inst. Math., vol. 90 (1967), Amer. Math. Soc., 1969. Zbl0176.19101MR36 #7157
3. [3] V. I. ARNOLD, Mathematical Methods in Classical Mechanics, Springer-Verlag, 1980. 
4. [4] A. AVEZ, Anosov diffeomorphisms, in Proceedings Int. Symp. on Topological Dynamics, Benjamin, 1968, 17-51. Zbl0203.26101MR38 #4646
5. [5] R. BISHOP and R. CRITTENDEN, Geometry of Manifolds, Academic Press, 1964. Zbl0132.16003MR29 #6401
6. [6] R. BOTT, On some formulas for the characteristic classes of group actions, in Springer Lect. Notes in Math., 652 (1978), 25-61. Zbl0393.57011MR80a:57011
7. [7] C. CAMACHO and A. LINS NETO, Geometric Theory of Foliations, Progress in Math. Birkhausser, Boston, Basel and Stuttgart, 1985. Zbl0568.57002MR87a:57029
8. [8] C. CROKE, Rigidity for surfaces of non-positive curvature, Comment. Math. Helv., 65 (1990), 150-169. Zbl0704.53035MR91d:53056
9. [9] G. D'AMBRA and M. GROMOV, Lectures on transformation groups : Geometry and Dynamics, Preprint, Inst. Hautes Etudes Sci., IHES/M/90/1, 1990. 
10. [10] P. EBERLEIN, When is a geodesic flow of Anosov type? I, Jour. Differential Geom., 8 (1973), 437-463. Zbl0285.58008MR52 #1788
11. [11] R. FERES, Geodesic flows on manifolds of negative curvature with smooth horospheric foliations, preprint, 1989. Zbl0727.58035
12. [12] R. FERES and A. KATOK, Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows, Ergodic Theory Dynamical Systems, 9 (1989), 427-432. Zbl0667.58050MR90k:58167
13. [13] R. FERES and A. KATOK, Anosov flows with smooth foliations and rigidity of geodesic flows in three dimensional manifolds, Ergodic Theory Dynamical Systems, 10 (1990), 657-670. Zbl0729.58039MR92e:58150
14. [14] L. FLAMINIO and A. KATOK, Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori, Ergodic Theory Dynamical Systems, 11 (1991), to appear. Zbl0725.58033MR93a:58133
15. [15] P. FOULON and F. LABOURIE, Flots d'Anosov à distributions de Liapunov différentiables, C. R. Acad. Sci. Paris, 309 (1989), 255-260. Zbl0674.58037MR91b:58189
16. [16] E. GHYS, Actions localement libres du groupe affine, Invent. Math., 82 (1985), 479-526. Zbl0577.57010MR87f:58084
17. [17] E. GHYS, Flots d'Anosov dont les feuilletages stables sont différentiables, Annales Ecole Norm. Sup., 20 (1987), 251-270. Zbl0663.58025MR89h:58153
18. [18] E. GHYS, Sur l'invariance topologique de la classe de Godbillon-Vey, Annales Inst. Fourier, 37 (4) (1987), 59-76. Zbl0633.58025MR89e:57023
19. [19] E. GHYS, Codimension-one Anosov flows and suspensions, in R. LABARCA, R. BAMON and J. PALIS, editors, Springer Lect. Notes Math., 1331 (1989), 59-72. Zbl0672.58033MR90a:58141
20. [20] E. GHYS, Sur l'invariant de Godbillon-Vey, in Séminaire Bourbaki, mars 1989, Astérisque, 177-178 (1990), 155-181. Zbl0707.57015MR91h:57015
21. [21] E. GHYS and T. TSUBOI, Différentiabilité des conjugaisons entre systèmes dynamiques de dimension 1, Annales Inst. Fourier, 38 (1) (1988), 215-244. Zbl0633.58018MR89i:58119
22. [22] C. GODBILLON and J. VEY, Un invariant de feuilletages de codimension 1, C. R. Acad. Sci. Paris, 273 (1971), 92-95. Zbl0215.24604MR44 #1046
23. [23] P. GRZIGORCHUK, On three-dimensional Anosov flows with C2-invariant foliations, preprint, 1988. 
24. [24] V. GUILLEMIN and D. KAZHDAN, On the cohomology of certain dynamical systems, Topology, 19 (1980), 291-299. Zbl0498.58018MR81j:58067
25. [25] V. GUILLEMIN and D. KAZHDAN, Some inverse spectral results for negatively curved 2-manifolds, Topology, 19 (1980), 301-313. Zbl0465.58027MR81j:58082
26. [26] U. HAMENSTADT, Entropy-rigidity of locally symmetric spaces of negative curvature, Annals of Math., 131 (1990), 35-51. Zbl0699.53049MR91d:58202
27. [27] U. HAMENSTADT, Metric and topological entropies of geodesic flows, preprint, 1990. 
28. [28] B. HASSELBLATT, Regularity of the Anosov splitting and of horospheric foliations, preprint, 1990. 
29. [29] M. HIRSCH and C. PUGH, Stable manifolds and hyperbolic sets, in Proc. Symp. Pure Math., Amer. Math. Soc. 14 (1970), 133-164. Zbl0215.53001MR42 #6872
30. [30] M. HIRSCH and C. PUGH, Smoothness of horocycle foliations, Jour. Differential Geom., 10 (1975), 225-238. Zbl0312.58008MR51 #4319
31. [31] S. HURDER, Characteristic classes for C1-foliations, preprint, 1990. Zbl0687.57010
32. [32] S. HURDER, Deformation rigidity for subgroups of SL(n, Z) acting on the n-torus, Bulletin Amer. Math. Soc., 23 (1990), 107-113. Zbl0713.57022MR91c:57048
33. [33] S. HURDER, Rigidity for Anosov actions of higher rank lattices, preprint, 1990. 
34. [34] J.-L. JOURNÉ, On a regularity problem occurring in connection with Anosov diffeomorphisms, Comm. Math. Phys., 106 (1986), 345-352. Zbl0603.58019MR88b:58103
35. [35] J.-L. JOURNÉ, A regularity lemma for functions of several variables, Revista Mat. Iber., 4 (2) (1988), 187-193. Zbl0699.58008MR91j:58123
36. [36] M. KANAI, Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations, Ergodic Theory Dynamical Systems, 8 (1988), 215-240. Zbl0634.58020MR89k:58230
37. [37] M. KANAI, Differential-geometric studies on dynamics of geodesic and frame flows, preprint, 1989. 
38. [38] A. KATOK, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Publ. Math. Inst. Hautes Etudes Sci., 51 (1980), 137-173. Zbl0445.58015MR81i:28022
39. [39] A. KATOK, Entropy and closed geodesics, Ergodic Theory Dynamical Systems, 2 (1982), 339-366. Zbl0525.58027MR85b:53047
40. [40] A. KATOK, Four applications of conformal equivalence to geometry and dynamics, Ergodic Theory Dynamical Systems, 8 (1988), 139-152. Zbl0668.58042MR89m:58165
41. [41] A. KATOK, Canonical cocycles for Anosov flows, to appear. 
42. [42] A. KATOK and J. LEWIS, Local rigidity for certain groups of toral automorphisms, preprint, 1990. Zbl0785.22012
43. [43] G. KNIEPER and H. WEISS, Smoothness of measure theoretic entropy for Anosov flows, preprint, 1989. Zbl0671.58021
44. [44] S. KRANTZ, Lipshitz spaces, smoothness of functions, and approximation theory, Expositions Mathematicae, 3 (1983), 193-260. Zbl0518.46018MR86g:41001
45. [45] A. LIVSIC, Homology properties of U-systems, Math. Notes of U.S.S.R., 10 (1971), 758-763. Zbl0235.58010MR45 #2746
46. [46] A. LIVSIC, Cohomology of dynamical systems, Math. U.S.S.R. Izvestija, 6 (1972), 1278-1301. Zbl0273.58013MR48 #12606
47. [47] A. LIVSIC and J. SINAI, On invariant measures compatible with the smooth structure for transitive U-systems, Soviet Math. Doklady, 13 (6) (1972), 1656-1659. Zbl0284.58014
48. [48] R. de LA LLAVÉ, Analytic regularity of solutions of Livsic's cohomology equation and some applications to analytic conjugacy of hyperbolic dynamical systems, Ergodic Theory Dynamical Systems, to appear. Zbl0883.58024
49. [49] R. de LA LLAVÉ, J. MARCO and R. MORIYON, Canonical perturbation theory of Anosov systems and regularity results for Livsic cohomology equation, Annals of Math., 123 (1986), 537-612. Zbl0603.58016MR88h:58091
50. [50] R. de LA LLAVÉ and R. MORIYON, Invariants for smooth conjugacy of hyperbolic dynamical systems, IV, Comm. Math. Phys., 116 (1988), 185-192. Zbl0673.58038MR90h:58064
51. [51] C. PUGH, M. HIRSCH and M. SHUB, Invariant Manifolds, Springer Lect. Notes Math., n° 583, 1977. Zbl0355.58009MR58 #18595
52. [52] J. M. MARCO and R. MORIYON, Invariants for smooth conjugacy of hyperbolic dynamical systems, III, Comm. Math. Phys., 112 (1987), 317-333. Zbl0673.58037MR89b:58168
53. [53] Y. MITSUMATSU, A relation between the topological invariance of the Godbillon-Vey invariant and the differentiability of Anosov foliations, in Foliations, vol. 5 of Advanced Studies in Pure Math., University of Tokyo Press, 1985. Zbl0653.57018MR88a:57050
54. [54] J. MOSER, The analytic invariants of an area-preserving mapping near a hyperbolic fixed-point, Comm. Pure and Applied Math., IX (1956), 673-692. Zbl0072.40801MR19,278b
55. [55] J.-P. OTAL, Le spectre marqué des longueurs des surfaces à courbure négative, Annals of Math., 131 (1990), 151-162. Zbl0699.58018MR91c:58026
56. [56] Ya. B. PESIN, Equations for the entropy of a geodesic flow on a compact Riemannian manifold without conjugacy points, Math. Notes U.S.S.R., 24 (1978), 796-805. Zbl0411.58016
57. [57] J. PLANTE, Anosov flows, American Jour. Math., 94 (1972), 729-755. Zbl0257.58007MR51 #14099
58. [58] G. RABY, Invariance de classes de Godbillon-Vey par C1-difféomorphismes, Annales Inst. Fourier, 38 (1) (1988), 205-213. Zbl0596.57018MR89j:57023
59. [59] E. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton, Princeton University Press, 1970. Zbl0207.13501MR44 #7280
60. [60] S. STERNBERG, The structure of local diffeomorphisms, III, American Jour. Math., 81 (1959), 578-604. Zbl0211.56304MR22 #738
61. [61] W. THURSTON, Noncobordant foliations of S3, Bulletin Amer. Math. Soc., 78 (1972), 511-514. Zbl0266.57004MR45 #7741
62. [62] W. THURSTON, Foliations and groups of diffeomorphisms, Bulletin Amer. Math. Soc., 80 (1974), 304-307. Zbl0295.57014MR49 #4027
63. [63] T. TSUBOI, Area functional and Godbillon-Vey cocycles, preprint, 1989. Zbl0759.57019
64. [64] T. TSUBOI, On the foliated products of class C1, Annals of Math., 130 (1989), 227-271. Zbl0701.57012MR91a:57028
65. [65] A. ZYGMUND, Trigonometric Series, Cambridge University Press, 1968. Zbl0085.05601MR38 #4882

1. Anatole Katok, Ralph J. Spatzier, First cohomology of Anosov actions of higher rank abelian groups and applications to rigidity
2. Frédéric Faure, Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula
3. Étienne Ghys, Déformations de flots d'Anosov et de groupes fuchsiens
4. Thierry Barbot, Plane affine geometry and Anosov flows
5. Yong Fang, Real and complex transversely symplectic Anosov flows of dimension five
6. Gabriel P. Paternain, Hyperbolic dynamics of Euler-Lagrange flows on prescribed energy levels
7. Takashi Tsuboi, Area functionals and Godbillon-Vey cocycles
8. Pierre Pansu, Le flot géodésique des variétés riemanniennes à courbure négative