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Bootstrapping regularity of the Anosov splitting. (English) Zbl 0790.58029
Summary: Finite smoothness of the Anosov splitting implies \(C^{\infty}\).

MSC:
37D99 Dynamical systems with hyperbolic behavior
37D40 Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
53D25 Geodesic flows in symplectic geometry and contact geometry
37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\)
53C12 Foliations (differential geometric aspects)
53C20 Global Riemannian geometry, including pinching
53C35 Differential geometry of symmetric spaces
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References:
[1] Yves Benoist, Patrick Foulon, and François Labourie, Flots d’Anosov a distributions stable et instable differentiables, École Polytechnique preprint M949.0690, 1990. · Zbl 0754.58027
[2] Renato Feres, Geodesic flows on manifolds of negative curvature with smooth horospheric foliations, Ergodic Theory Dynam. Systems 11 (1991), no. 4, 653 – 686. · Zbl 0727.58035 · doi:10.1017/S0143385700006416 · doi.org
[3] Renato Feres and Anatole Katok, Anosov flows with smooth foliations and rigidity of geodesic flows on three-dimensional manifolds of negative curvature, Ergodic Theory Dynam. Systems 10 (1990), no. 4, 657 – 670. · Zbl 0729.58039 · doi:10.1017/S0143385700005836 · doi.org
[4] Étienne Ghys, Codimension one Anosov flows and suspensions, Dynamical systems, Valparaiso 1986, Lecture Notes in Math., vol. 1331, Springer, Berlin, 1988, pp. 59 – 72. · Zbl 0672.58033 · doi:10.1007/BFb0083066 · doi.org
[5] Etienne Ghys, Déformations de flots d’Anosov et de groupes Fuchsiens, Annales de l’Institut Fourier (1992) (to appear). · Zbl 0759.58036
[6] Borís Hasselblatt, Regularity of the Anosov splitting and of horospheric foliations, preprint IHES/M/91/1, 1991.
[7] S. Hurder and A. Katok, Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Inst. Hautes Études Sci. Publ. Math. 72 (1990), 5 – 61 (1991). · Zbl 0725.58034
[8] J.-L. Journé, A regularity lemma for functions of several variables, Rev. Mat. Iberoamericana 4 (1988), no. 2, 187 – 193. · Zbl 0699.58008 · doi:10.4171/RMI/69 · doi.org
[9] Masahiko Kanai, Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations, Ergodic Theory Dynam. Systems 8 (1988), no. 2, 215 – 239. · Zbl 0634.58020 · doi:10.1017/S0143385700004430 · doi.org
[10] Wilhelm Klingenberg, Riemannian geometry, de Gruyter Studies in Mathematics, vol. 1, Walter de Gruyter & Co., Berlin-New York, 1982. · Zbl 0495.53036
[11] R. de la Llave, J. M. Marco, and R. Moriyón, Canonical perturbation theory of Anosov systems and regularity results for the Livšic cohomology equation, Ann. of Math. (2) 123 (1986), no. 3, 537 – 611. · Zbl 0603.58016 · doi:10.2307/1971334 · doi.org
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