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Minimality of the horocycle flow on laminations by hyperbolic surfaces with non-trivial topology
1. | GeoDynApp - ECSING Group, Spain |
2. | Institut de Recherche Mathématiques de Rennes, Université de Rennes 1, F-35042 Rennes, France |
3. | Instituto de Matemática y Estadística Rafael Laguardia, Facultad de Ingeniería, Universidad de la República, J. Herrera y Reissig 565, C.P. 11300 Montevideo |
4. | Universidad Nacional Autónoma de México, Apartado Postal 273, Admon. de correos #3, C.P. 62251 Cuernavaca, Morelos |
References:
[1] |
F. Alcalde Cuesta and F. Dal'Bo, Remarks on the dynamics of the horocycle flow for homogeneous foliations by hyperbolic surfaces,, Expo. Math., 33 (2015), 431.
doi: 10.1016/j.exmath.2015.07.006. |
[2] |
S. Alvarez and P. Lessa, The Teichmüller space of the Hirsch foliation,, preprint, (). Google Scholar |
[3] |
Ch. Bonatti, X. Gómez-Mont and R. Vila-Freyer, Statistical behaviour of the leaves of Riccati foliations,, Ergodic Theory Dynam. Systems, 30 (2010), 67.
doi: 10.1017/S0143385708001028. |
[4] |
A. Candel, Uniformization of surface laminations,, Ann. Sci. École Norm. Sup., 26 (1993), 489.
|
[5] |
A. Candel and L. Conlon, Foliations. I,, Graduate Studies in Mathematics, (2000).
|
[6] |
J. Cheeger, M. Gromov and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds,, J. Differential Geom., 17 (1982), 15.
|
[7] |
F. Dal'bo, Topologie du feuilletage fortement stable,, Ann. Inst. Fourier (Grenoble), 50 (2000), 981.
doi: 10.5802/aif.1781. |
[8] |
F. Dal'Bo, Geodesic and Horocyclic Trajectories,, Universitext. Translated from the 2007 French original, (2007).
doi: 10.1007/978-0-85729-073-1. |
[9] |
D. B. A. Epstein, K. C. Millett and D. Tischler, Leaves without holonomy,, J. London Math. Soc. (2), 16 (1977), 548.
|
[10] |
G. Hector, Feuilletages en cylindres,, in Geometry and topology (Proc. III Latin Amer. School of Math., (1977), 252.
|
[11] |
G. Hector, S. Matsumoto and G. Meigniez, Ends of leaves of Lie foliations,, J. Math. Soc. Japan, 57 (2005), 753.
doi: 10.2969/jmsj/1158241934. |
[12] |
G. A. Hedlund, Fuchsian groups and transitive horocycles,, Duke Math. J., 2 (1936), 530.
doi: 10.1215/S0012-7094-36-00246-6. |
[13] |
M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds,, Lecture Notes in Mathematics, (1977).
|
[14] |
S. Hurder, Ergodic theory of foliations and a theorem of Sacksteder,, in Dynamical systems (College Park, 1342 (1988), 1986.
doi: 10.1007/BFb0082838. |
[15] |
V. A. Kaimanovich, Ergodic properties of the horocycle flow and classification of Fuchsian groups,, J. Dynam. Control Systems, 6 (2000), 21.
doi: 10.1023/A:1009517621605. |
[16] |
M. Kulikov, The horocycle flow without minimal sets,, C. R. Math. Acad. Sci. Paris, 338 (2004), 477.
doi: 10.1016/j.crma.2003.12.027. |
[17] |
M. Martínez, S. Matsumoto and A. Verjovsky, Horocycle flows for laminations by hyperbolic Riemann surfaces and Hedlund's theorem,, to appear in Journal of Modern Dynamics, 10 (2016). Google Scholar |
[18] |
S. Matsumoto, Dynamical systems without minimal sets,, preprint, (). Google Scholar |
[19] |
S. Matsumoto, Horocycle flows without minimal sets,, preprint, (). Google Scholar |
[20] |
T. Roblin, Ergodicitéet équidistribution en courbure négative,, Mém. Soc. Math. Fr. (N.S.), 95 (2003).
|
[21] |
A. Sambusetti, Asymptotic properties of coverings in negative curvature,, Geom. Topol., 12 (2008), 617.
doi: 10.2140/gt.2008.12.617. |
[22] |
O. Sarig, The horocyclic flow and the Laplacian on hyperbolic surfaces of infinite genus,, Geom. Funct. Anal., 19 (2010), 1757.
doi: 10.1007/s00039-010-0048-9. |
[23] |
A. N. Starkov, Fuchsian groups from the dynamical viewpoint,, J. Dynam. Control Systems, 1 (1995), 427.
doi: 10.1007/BF02269378. |
[24] |
A. Verjovsky, A uniformization theorem for holomorphic foliations,, in The Lefschetz centennial conference, (1984), 233.
|
show all references
References:
[1] |
F. Alcalde Cuesta and F. Dal'Bo, Remarks on the dynamics of the horocycle flow for homogeneous foliations by hyperbolic surfaces,, Expo. Math., 33 (2015), 431.
doi: 10.1016/j.exmath.2015.07.006. |
[2] |
S. Alvarez and P. Lessa, The Teichmüller space of the Hirsch foliation,, preprint, (). Google Scholar |
[3] |
Ch. Bonatti, X. Gómez-Mont and R. Vila-Freyer, Statistical behaviour of the leaves of Riccati foliations,, Ergodic Theory Dynam. Systems, 30 (2010), 67.
doi: 10.1017/S0143385708001028. |
[4] |
A. Candel, Uniformization of surface laminations,, Ann. Sci. École Norm. Sup., 26 (1993), 489.
|
[5] |
A. Candel and L. Conlon, Foliations. I,, Graduate Studies in Mathematics, (2000).
|
[6] |
J. Cheeger, M. Gromov and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds,, J. Differential Geom., 17 (1982), 15.
|
[7] |
F. Dal'bo, Topologie du feuilletage fortement stable,, Ann. Inst. Fourier (Grenoble), 50 (2000), 981.
doi: 10.5802/aif.1781. |
[8] |
F. Dal'Bo, Geodesic and Horocyclic Trajectories,, Universitext. Translated from the 2007 French original, (2007).
doi: 10.1007/978-0-85729-073-1. |
[9] |
D. B. A. Epstein, K. C. Millett and D. Tischler, Leaves without holonomy,, J. London Math. Soc. (2), 16 (1977), 548.
|
[10] |
G. Hector, Feuilletages en cylindres,, in Geometry and topology (Proc. III Latin Amer. School of Math., (1977), 252.
|
[11] |
G. Hector, S. Matsumoto and G. Meigniez, Ends of leaves of Lie foliations,, J. Math. Soc. Japan, 57 (2005), 753.
doi: 10.2969/jmsj/1158241934. |
[12] |
G. A. Hedlund, Fuchsian groups and transitive horocycles,, Duke Math. J., 2 (1936), 530.
doi: 10.1215/S0012-7094-36-00246-6. |
[13] |
M. W. Hirsch, C. C. Pugh and M. Shub, Invariant Manifolds,, Lecture Notes in Mathematics, (1977).
|
[14] |
S. Hurder, Ergodic theory of foliations and a theorem of Sacksteder,, in Dynamical systems (College Park, 1342 (1988), 1986.
doi: 10.1007/BFb0082838. |
[15] |
V. A. Kaimanovich, Ergodic properties of the horocycle flow and classification of Fuchsian groups,, J. Dynam. Control Systems, 6 (2000), 21.
doi: 10.1023/A:1009517621605. |
[16] |
M. Kulikov, The horocycle flow without minimal sets,, C. R. Math. Acad. Sci. Paris, 338 (2004), 477.
doi: 10.1016/j.crma.2003.12.027. |
[17] |
M. Martínez, S. Matsumoto and A. Verjovsky, Horocycle flows for laminations by hyperbolic Riemann surfaces and Hedlund's theorem,, to appear in Journal of Modern Dynamics, 10 (2016). Google Scholar |
[18] |
S. Matsumoto, Dynamical systems without minimal sets,, preprint, (). Google Scholar |
[19] |
S. Matsumoto, Horocycle flows without minimal sets,, preprint, (). Google Scholar |
[20] |
T. Roblin, Ergodicitéet équidistribution en courbure négative,, Mém. Soc. Math. Fr. (N.S.), 95 (2003).
|
[21] |
A. Sambusetti, Asymptotic properties of coverings in negative curvature,, Geom. Topol., 12 (2008), 617.
doi: 10.2140/gt.2008.12.617. |
[22] |
O. Sarig, The horocyclic flow and the Laplacian on hyperbolic surfaces of infinite genus,, Geom. Funct. Anal., 19 (2010), 1757.
doi: 10.1007/s00039-010-0048-9. |
[23] |
A. N. Starkov, Fuchsian groups from the dynamical viewpoint,, J. Dynam. Control Systems, 1 (1995), 427.
doi: 10.1007/BF02269378. |
[24] |
A. Verjovsky, A uniformization theorem for holomorphic foliations,, in The Lefschetz centennial conference, (1984), 233.
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