@article{PMIHES_1990__72__5_0,
author = {Hurder, S. and Katok, Anatoly},
title = {Differentiability, rigidity and {Godbillon-Vey} classes for {Anosov} flows},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {5--61},
publisher = {Institut des Hautes Etudes Scientifiques},
volume = {72},
year = {1990},
mrnumber = {92b:58179},
zbl = {0725.58034},
language = {en},
url = {https://www.numdam.org/item/PMIHES_1990__72__5_0/}
}
TY - JOUR AU - Hurder, S. AU - Katok, Anatoly TI - Differentiability, rigidity and Godbillon-Vey classes for Anosov flows JO - Publications Mathématiques de l'IHÉS PY - 1990 SP - 5 EP - 61 VL - 72 PB - Institut des Hautes Etudes Scientifiques UR - https://www.numdam.org/item/PMIHES_1990__72__5_0/ LA - en ID - PMIHES_1990__72__5_0 ER -
%0 Journal Article %A Hurder, S. %A Katok, Anatoly %T Differentiability, rigidity and Godbillon-Vey classes for Anosov flows %J Publications Mathématiques de l'IHÉS %D 1990 %P 5-61 %V 72 %I Institut des Hautes Etudes Scientifiques %U https://www.numdam.org/item/PMIHES_1990__72__5_0/ %G en %F PMIHES_1990__72__5_0
Hurder, S.; Katok, Anatoly. Differentiability, rigidity and Godbillon-Vey classes for Anosov flows. Publications Mathématiques de l'IHÉS, Volume 72 (1990), pp. 5-61. https://www.numdam.org/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. | Zbl | MR
[2] , Geodesic Flows on Closed Riemannian Manifolds with Negative Curvature, Proc. Steklov Inst. Math., vol. 90 (1967), Amer. Math. Soc., 1969. | Zbl | MR
[3] , Mathematical Methods in Classical Mechanics, Springer-Verlag, 1980.
[4] , Anosov diffeomorphisms, in Proceedings Int. Symp. on Topological Dynamics, Benjamin, 1968, 17-51. | Zbl | MR
[5] and , Geometry of Manifolds, Academic Press, 1964. | Zbl | MR
[6] , On some formulas for the characteristic classes of group actions, in Springer Lect. Notes in Math., 652 (1978), 25-61. | Zbl | MR
[7] and , Geometric Theory of Foliations, Progress in Math. Birkhausser, Boston, Basel and Stuttgart, 1985. | Zbl | MR
[8] , Rigidity for surfaces of non-positive curvature, Comment. Math. Helv., 65 (1990), 150-169. | Zbl | MR
[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. | Zbl | MR
[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. | Zbl | MR
[13] and , Anosov flows with smooth foliations and rigidity of geodesic flows in three dimensional manifolds, Ergodic Theory Dynamical Systems, 10 (1990), 657-670. | Zbl | MR
[14] and , Rigidity of symplectic Anosov diffeomorphisms on low dimensional tori, Ergodic Theory Dynamical Systems, 11 (1991), to appear. | Zbl | MR
[15] and , Flots d'Anosov à distributions de Liapunov différentiables, C. R. Acad. Sci. Paris, 309 (1989), 255-260. | Zbl | MR
[16] , Actions localement libres du groupe affine, Invent. Math., 82 (1985), 479-526. | Zbl | MR
[17] , Flots d'Anosov dont les feuilletages stables sont différentiables, Annales Ecole Norm. Sup., 20 (1987), 251-270. | Zbl | MR | Numdam
[18] , Sur l'invariance topologique de la classe de Godbillon-Vey, Annales Inst. Fourier, 37 (4) (1987), 59-76. | Zbl | MR | Numdam
[19] , Codimension-one Anosov flows and suspensions, in R. LABARCA, R. BAMON and J. PALIS, editors, Springer Lect. Notes Math., 1331 (1989), 59-72. | Zbl | MR
[20] , Sur l'invariant de Godbillon-Vey, in Séminaire Bourbaki, mars 1989, Astérisque, 177-178 (1990), 155-181. | Zbl | MR | Numdam
[21] and , Différentiabilité des conjugaisons entre systèmes dynamiques de dimension 1, Annales Inst. Fourier, 38 (1) (1988), 215-244. | Zbl | MR | Numdam
[22] and , Un invariant de feuilletages de codimension 1, C. R. Acad. Sci. Paris, 273 (1971), 92-95. | Zbl | MR
[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. | Zbl | MR
[25] and , Some inverse spectral results for negatively curved 2-manifolds, Topology, 19 (1980), 301-313. | Zbl | MR
[26] , Entropy-rigidity of locally symmetric spaces of negative curvature, Annals of Math., 131 (1990), 35-51. | Zbl | MR
[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. | Zbl | MR
[30] and , Smoothness of horocycle foliations, Jour. Differential Geom., 10 (1975), 225-238. | Zbl | MR
[31] , Characteristic classes for C1-foliations, preprint, 1990. | Zbl
[32] , Deformation rigidity for subgroups of SL(n, Z) acting on the n-torus, Bulletin Amer. Math. Soc., 23 (1990), 107-113. | Zbl | MR
[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. | Zbl | MR
[35] , A regularity lemma for functions of several variables, Revista Mat. Iber., 4 (2) (1988), 187-193. | Zbl | MR
[36] , Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations, Ergodic Theory Dynamical Systems, 8 (1988), 215-240. | Zbl | MR
[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. | Zbl | MR | Numdam
[39] , Entropy and closed geodesics, Ergodic Theory Dynamical Systems, 2 (1982), 339-366. | Zbl | MR
[40] , Four applications of conformal equivalence to geometry and dynamics, Ergodic Theory Dynamical Systems, 8 (1988), 139-152. | Zbl | MR
[41] , Canonical cocycles for Anosov flows, to appear.
[42] and , Local rigidity for certain groups of toral automorphisms, preprint, 1990. | Zbl
[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. | Zbl | MR
[45] , Homology properties of U-systems, Math. Notes of U.S.S.R., 10 (1971), 758-763. | Zbl | MR
[46] , Cohomology of dynamical systems, Math. U.S.S.R. Izvestija, 6 (1972), 1278-1301. | Zbl | MR
[47] and , On invariant measures compatible with the smooth structure for transitive U-systems, Soviet Math. Doklady, 13 (6) (1972), 1656-1659. | Zbl
[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
[49] , and , Canonical perturbation theory of Anosov systems and regularity results for Livsic cohomology equation, Annals of Math., 123 (1986), 537-612. | Zbl | MR
[50] and , Invariants for smooth conjugacy of hyperbolic dynamical systems, IV, Comm. Math. Phys., 116 (1988), 185-192. | Zbl | MR
[51] , and , Invariant Manifolds, Springer Lect. Notes Math., n° 583, 1977. | Zbl | MR
[52] and , Invariants for smooth conjugacy of hyperbolic dynamical systems, III, Comm. Math. Phys., 112 (1987), 317-333. | Zbl | MR
[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. | Zbl | MR
[54] , The analytic invariants of an area-preserving mapping near a hyperbolic fixed-point, Comm. Pure and Applied Math., IX (1956), 673-692. | Zbl | MR
[55] , Le spectre marqué des longueurs des surfaces à courbure négative, Annals of Math., 131 (1990), 151-162. | Zbl | MR
[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
[57] , Anosov flows, American Jour. Math., 94 (1972), 729-755. | Zbl | MR
[58] , Invariance de classes de Godbillon-Vey par C1-difféomorphismes, Annales Inst. Fourier, 38 (1) (1988), 205-213. | Zbl | MR | Numdam
[59] , Singular Integrals and Differentiability Properties of Functions, Princeton, Princeton University Press, 1970. | Zbl | MR
[60] , The structure of local diffeomorphisms, III, American Jour. Math., 81 (1959), 578-604. | Zbl | MR
[61] , Noncobordant foliations of S3, Bulletin Amer. Math. Soc., 78 (1972), 511-514. | Zbl | MR
[62] , Foliations and groups of diffeomorphisms, Bulletin Amer. Math. Soc., 80 (1974), 304-307. | Zbl | MR
[63] , Area functional and Godbillon-Vey cocycles, preprint, 1989. | Zbl | Numdam
[64] , On the foliated products of class C1, Annals of Math., 130 (1989), 227-271. | Zbl | MR
[65] , Trigonometric Series, Cambridge University Press, 1968. | Zbl | MR






