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Counterexamples in non-positive curvature
1. | Université de Bretagne Occidentale, 6 av. Le Gorgeu, 29238 Brest cedex, France |
2. | LAMFA, Université Picardie Jules Verne, 33 rue St Leu 80000 Amiens, France |
References:
[1] |
D. V. Anosov, Geodesic flows on closed riemannian manifolds with negative curvature, Proc. Steklov Inst. Math., 90 (1967). |
[2] |
W. Ballmann, M. Brin and R. Spatzier, Structure of manifolds of nonpositive curvature. II, Ann. of Math., 122 (1985), 205-235.
doi: 10.2307/1971303. |
[3] |
P. Billingsley, Convergence of probability measures, "Wiley Series in Probability and Statistics: Probability and Statistics," 2nd edition, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1999. |
[4] |
Yu. D. Burago and S. Z. Shefel, The geometry of surfaces in Euclidean spaces, "Geometry, III," Encyclopaedia Math. Sci., 48, Springer, Berlin, (1992), 1-85, 251-256. |
[5] |
Y. Coudene and B. Schapira, Generic measures for hyperbolic flows on non-compact spaces, Israel J. Math., 179 (2010), 157-172.
doi: 10.1007/s11856-010-0076-z. |
[6] |
P. Eberlein, Geodesic flows on negatively curved manifolds I, Ann. Math. II Ser., 95 (1972), 492-510.
doi: 10.2307/1970869. |
[7] |
P. Eberlein, "Geometry of Nonpositively Curved Manifolds," Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1996, vii+449. |
[8] |
J. Hadamard, Les surfaces courbures opposées et leurs lignes géodésiques, dans Oeuvres (1898), 2, 729-775, Paris: Editions du Centre National de la Recherche Scientifique, (1968), 2296. |
[9] |
G. Knieper, Hyperbolic dynamics and Riemannian geometry, Handbook of Dynamical Systems, 1A (2002), 453-545. |
[10] |
G. Link, M. Peigné and J. C. Picaud, Sur les surfaces non-compactes de rang un, L'enseignement Mathématique, 52 (2006), 3-36. |
[11] |
C. Robinson, Dynamical systems. Stability, symbolic dynamics, and chaos, "Studies in Advanced Mathematics," 2nd edition, CRC Press, Boca Raton, FL, 1999. |
[12] |
K. Sigmund, On the space of invariant measures for hyperbolic flows, Amer. J. Math., 94 (1972), 31-37.
doi: 10.2307/2373591. |
show all references
References:
[1] |
D. V. Anosov, Geodesic flows on closed riemannian manifolds with negative curvature, Proc. Steklov Inst. Math., 90 (1967). |
[2] |
W. Ballmann, M. Brin and R. Spatzier, Structure of manifolds of nonpositive curvature. II, Ann. of Math., 122 (1985), 205-235.
doi: 10.2307/1971303. |
[3] |
P. Billingsley, Convergence of probability measures, "Wiley Series in Probability and Statistics: Probability and Statistics," 2nd edition, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1999. |
[4] |
Yu. D. Burago and S. Z. Shefel, The geometry of surfaces in Euclidean spaces, "Geometry, III," Encyclopaedia Math. Sci., 48, Springer, Berlin, (1992), 1-85, 251-256. |
[5] |
Y. Coudene and B. Schapira, Generic measures for hyperbolic flows on non-compact spaces, Israel J. Math., 179 (2010), 157-172.
doi: 10.1007/s11856-010-0076-z. |
[6] |
P. Eberlein, Geodesic flows on negatively curved manifolds I, Ann. Math. II Ser., 95 (1972), 492-510.
doi: 10.2307/1970869. |
[7] |
P. Eberlein, "Geometry of Nonpositively Curved Manifolds," Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1996, vii+449. |
[8] |
J. Hadamard, Les surfaces courbures opposées et leurs lignes géodésiques, dans Oeuvres (1898), 2, 729-775, Paris: Editions du Centre National de la Recherche Scientifique, (1968), 2296. |
[9] |
G. Knieper, Hyperbolic dynamics and Riemannian geometry, Handbook of Dynamical Systems, 1A (2002), 453-545. |
[10] |
G. Link, M. Peigné and J. C. Picaud, Sur les surfaces non-compactes de rang un, L'enseignement Mathématique, 52 (2006), 3-36. |
[11] |
C. Robinson, Dynamical systems. Stability, symbolic dynamics, and chaos, "Studies in Advanced Mathematics," 2nd edition, CRC Press, Boca Raton, FL, 1999. |
[12] |
K. Sigmund, On the space of invariant measures for hyperbolic flows, Amer. J. Math., 94 (1972), 31-37.
doi: 10.2307/2373591. |
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