@article{PMIHES_1990__72__5_0,
author = {Hurder, Steven and Katok, Anatole},
title = {Differentiability, rigidity and Godbillon-Vey classes for Anosov flows},
journal = {Publications Math\'ematiques de l'IH\'ES},
volume = {72},
year = {1990},
pages = {5-61},
mrnumber = {92b:58179},
zbl = {0725.58034},
language = {en},
url = {http://dml.mathdoc.fr/item/PMIHES_1990__72__5_0}
}
Hurder, S.; Katok, Anatoly. Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Publications Mathématiques de l'IHÉS, Tome 72 (1990) pp. 5-61. http://gdmltest.u-ga.fr/item/PMIHES_1990__72__5_0/
[1] , Tangent fields of transversal foliations in U-systems, Math. Notes Acad. Sci., USSR, 2 (5) (1967), 818-823. | MR 39 #3523 | Zbl 0171.42201
[2] , Geodesic Flows on Closed Riemannian Manifolds with Negative Curvature, Proc. Steklov Inst. Math., vol. 90 (1967), Amer. Math. Soc., 1969. | MR 36 #7157 | Zbl 0176.19101
[3] , Mathematical Methods in Classical Mechanics, Springer-Verlag, 1980.
[4] , Anosov diffeomorphisms, in Proceedings Int. Symp. on Topological Dynamics, Benjamin, 1968, 17-51. | MR 38 #4646 | Zbl 0203.26101
[5] and , Geometry of Manifolds, Academic Press, 1964. | MR 29 #6401 | Zbl 0132.16003
[6] , On some formulas for the characteristic classes of group actions, in Springer Lect. Notes in Math., 652 (1978), 25-61. | MR 80a:57011 | Zbl 0393.57011
[7] and , Geometric Theory of Foliations, Progress in Math. Birkhausser, Boston, Basel and Stuttgart, 1985. | MR 87a:57029 | Zbl 0568.57002
[8] , Rigidity for surfaces of non-positive curvature, Comment. Math. Helv., 65 (1990), 150-169. | MR 91d:53056 | Zbl 0704.53035
[9] and , Lectures on transformation groups : Geometry and Dynamics, Preprint, Inst. Hautes Etudes Sci., IHES/M/90/1, 1990.
[10] , When is a geodesic flow of Anosov type? I, Jour. Differential Geom., 8 (1973), 437-463. | MR 52 #1788 | Zbl 0285.58008
[11] , Geodesic flows on manifolds of negative curvature with smooth horospheric foliations, preprint, 1989.
[12] and , Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows, Ergodic Theory Dynamical Systems, 9 (1989), 427-432. | MR 90k:58167 | Zbl 0667.58050
[13] and , Anosov flows with smooth foliations and rigidity of geodesic flows in three dimensional manifolds, Ergodic Theory Dynamical Systems, 10 (1990), 657-670. | MR 92e:58150 | Zbl 0729.58039
[14] and , Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori, Ergodic Theory Dynamical Systems, 11 (1991), to appear. | MR 93a:58133 | Zbl 0725.58033
[15] and , Flots d'Anosov à distributions de Liapunov différentiables, C. R. Acad. Sci. Paris, 309 (1989), 255-260. | MR 91b:58189 | Zbl 0674.58037
[16] , Actions localement libres du groupe affine, Invent. Math., 82 (1985), 479-526. | MR 87f:58084 | Zbl 0577.57010
[17] , Flots d'Anosov dont les feuilletages stables sont différentiables, Annales Ecole Norm. Sup., 20 (1987), 251-270. | Numdam | MR 89h:58153 | Zbl 0663.58025
[18] , Sur l'invariance topologique de la classe de Godbillon-Vey, Annales Inst. Fourier, 37 (4) (1987), 59-76. | Numdam | MR 89e:57023 | Zbl 0633.58025
[19] , Codimension-one Anosov flows and suspensions, in R. LABARCA, R. BAMON and J. PALIS, editors, Springer Lect. Notes Math., 1331 (1989), 59-72. | MR 90a:58141 | Zbl 0672.58033
[20] , Sur l'invariant de Godbillon-Vey, in Séminaire Bourbaki, mars 1989, Astérisque, 177-178 (1990), 155-181. | Numdam | MR 91h:57015 | Zbl 0707.57015
[21] and , Différentiabilité des conjugaisons entre systèmes dynamiques de dimension 1, Annales Inst. Fourier, 38 (1) (1988), 215-244. | Numdam | MR 89i:58119 | Zbl 0633.58018
[22] and , Un invariant de feuilletages de codimension 1, C. R. Acad. Sci. Paris, 273 (1971), 92-95. | MR 44 #1046 | Zbl 0215.24604
[23] , On three-dimensional Anosov flows with C2-invariant foliations, preprint, 1988.
[24] and , On the cohomology of certain dynamical systems, Topology, 19 (1980), 291-299. | MR 81j:58067 | Zbl 0498.58018
[25] and , Some inverse spectral results for negatively curved 2-manifolds, Topology, 19 (1980), 301-313. | MR 81j:58082 | Zbl 0465.58027
[26] , Entropy-rigidity of locally symmetric spaces of negative curvature, Annals of Math., 131 (1990), 35-51. | MR 91d:58202 | Zbl 0699.53049
[27] , Metric and topological entropies of geodesic flows, preprint, 1990.
[28] , Regularity of the Anosov splitting and of horospheric foliations, preprint, 1990.
[29] and , Stable manifolds and hyperbolic sets, in Proc. Symp. Pure Math., Amer. Math. Soc. 14 (1970), 133-164. | MR 42 #6872 | Zbl 0215.53001
[30] and , Smoothness of horocycle foliations, Jour. Differential Geom., 10 (1975), 225-238. | MR 51 #4319 | Zbl 0312.58008
[31] , Characteristic classes for C1-foliations, preprint, 1990. | Zbl 0687.57010
[32] , Deformation rigidity for subgroups of SL(n, Z) acting on the n-torus, Bulletin Amer. Math. Soc., 23 (1990), 107-113. | MR 91c:57048 | Zbl 0713.57022
[33] , Rigidity for Anosov actions of higher rank lattices, preprint, 1990.
[34] , On a regularity problem occurring in connection with Anosov diffeomorphisms, Comm. Math. Phys., 106 (1986), 345-352. | MR 88b:58103 | Zbl 0603.58019
[35] , A regularity lemma for functions of several variables, Revista Mat. Iber., 4 (2) (1988), 187-193. | MR 91j:58123 | Zbl 0699.58008
[36] , Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations, Ergodic Theory Dynamical Systems, 8 (1988), 215-240. | MR 89k:58230 | Zbl 0634.58020
[37] , Differential-geometric studies on dynamics of geodesic and frame flows, preprint, 1989.
[38] , Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Publ. Math. Inst. Hautes Etudes Sci., 51 (1980), 137-173. | Numdam | MR 81i:28022 | Zbl 0445.58015
[39] , Entropy and closed geodesics, Ergodic Theory Dynamical Systems, 2 (1982), 339-366. | MR 85b:53047 | Zbl 0525.58027
[40] , Four applications of conformal equivalence to geometry and dynamics, Ergodic Theory Dynamical Systems, 8 (1988), 139-152. | MR 89m:58165 | Zbl 0668.58042
[41] , Canonical cocycles for Anosov flows, to appear.
[42] and , Local rigidity for certain groups of toral automorphisms, preprint, 1990. | Zbl 0785.22012
[43] and , Smoothness of measure theoretic entropy for Anosov flows, preprint, 1989.
[44] , Lipshitz spaces, smoothness of functions, and approximation theory, Expositions Mathematicae, 3 (1983), 193-260. | MR 86g:41001 | Zbl 0518.46018
[45] , Homology properties of U-systems, Math. Notes of U.S.S.R., 10 (1971), 758-763. | MR 45 #2746 | Zbl 0235.58010
[46] , Cohomology of dynamical systems, Math. U.S.S.R. Izvestija, 6 (1972), 1278-1301. | MR 48 #12606 | Zbl 0273.58013
[47] and , On invariant measures compatible with the smooth structure for transitive U-systems, Soviet Math. Doklady, 13 (6) (1972), 1656-1659. | Zbl 0284.58014
[48] , 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. | Zbl 0883.58024
[49] , and , Canonical perturbation theory of Anosov systems and regularity results for Livsic cohomology equation, Annals of Math., 123 (1986), 537-612. | MR 88h:58091 | Zbl 0603.58016
[50] and , Invariants for smooth conjugacy of hyperbolic dynamical systems, IV, Comm. Math. Phys., 116 (1988), 185-192. | MR 90h:58064 | Zbl 0673.58038
[51] , and , Invariant Manifolds, Springer Lect. Notes Math., n° 583, 1977. | MR 58 #18595 | Zbl 0355.58009
[52] and , Invariants for smooth conjugacy of hyperbolic dynamical systems, III, Comm. Math. Phys., 112 (1987), 317-333. | MR 89b:58168 | Zbl 0673.58037
[53] , 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. | MR 88a:57050 | Zbl 0653.57018
[54] , The analytic invariants of an area-preserving mapping near a hyperbolic fixed-point, Comm. Pure and Applied Math., IX (1956), 673-692. | MR 19,278b | Zbl 0072.40801
[55] , Le spectre marqué des longueurs des surfaces à courbure négative, Annals of Math., 131 (1990), 151-162. | MR 91c:58026 | Zbl 0699.58018
[56] , 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. | Zbl 0411.58016
[57] , Anosov flows, American Jour. Math., 94 (1972), 729-755. | MR 51 #14099 | Zbl 0257.58007
[58] , Invariance de classes de Godbillon-Vey par C1-difféomorphismes, Annales Inst. Fourier, 38 (1) (1988), 205-213. | Numdam | MR 89j:57023 | Zbl 0596.57018
[59] , Singular Integrals and Differentiability Properties of Functions, Princeton, Princeton University Press, 1970. | MR 44 #7280 | Zbl 0207.13501
[60] , The structure of local diffeomorphisms, III, American Jour. Math., 81 (1959), 578-604. | MR 22 #738 | Zbl 0211.56304
[61] , Noncobordant foliations of S3, Bulletin Amer. Math. Soc., 78 (1972), 511-514. | MR 45 #7741 | Zbl 0266.57004
[62] , Foliations and groups of diffeomorphisms, Bulletin Amer. Math. Soc., 80 (1974), 304-307. | MR 49 #4027 | Zbl 0295.57014
[63] , Area functional and Godbillon-Vey cocycles, preprint, 1989. | Numdam | Zbl 0759.57019
[64] , On the foliated products of class C1, Annals of Math., 130 (1989), 227-271. | MR 91a:57028 | Zbl 0701.57012
[65] , Trigonometric Series, Cambridge University Press, 1968. | MR 38 #4882 | Zbl 0085.05601