Geometry & Topology Volume 17, issue 2 (2013)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

Contact Anosov flows on hyperbolic 3–manifolds

Patrick Foulon and Boris Hasselblatt

Geometry & Topology 17 (2013) 1225–1252

DOI: 10.2140/gt.2013.17.1225

Bibliography

1	E Artin, Ein mechanisches System mit quasiergodischen Bahnen, Abh. Math. Semin. Univ. Hamb. 3 (1924) 170
2	T Barbot, Caractérisation des flots d'Anosov en dimension 3 par leurs feuilletages faibles, Ergodic Theory Dynam. Systems 15 (1995) 247 MR1332403
3	T Barbot, Generalizations of the Bonatti–Langevin example of Anosov flow and their classification up to topological equivalence, Comm. Anal. Geom. 6 (1998) 749 MR1652255
4	T Barbot, Plane affine geometry and Anosov flows, Ann. Sci. École Norm. Sup. 34 (2001) 871 MR1872423
5	T Barbot, De l'hyperbolique au globalement hyperbolique, Habilitation à diriger des recherches, Université Claude Bernard de Lyon (2005)
6	T Barthelmé, A new Laplace operator in Finsler geometry and periodic orbits of Anosov flows, PhD thesis, Université de Strasbourg (2012) arXiv:1204.0879
7	T Barthelmé, S R Fenley, Knot theory of $R$–covered Anosov flows: Homotopy versus isotopy of closed orbits arXiv:1208.6487
8	Y Benoist, P Foulon, F Labourie, Flots d'Anosov à distributions de Liapounov différentiables, I, Ann. Inst. H. Poincaré Phys. Théor. 53 (1990) 395 MR1096099
9	Y Benoist, P Foulon, F Labourie, Flots d'Anosov à distributions stable et instable différentiables, J. Amer. Math. Soc. 5 (1992) 33 MR1124979
10	C Bonatti, R Langevin, Un exemple de flot d'Anosov transitif transverse à un tore et non conjugué à une suspension, Ergodic Theory Dynam. Systems 14 (1994) 633 MR1304136
11	D Calegari, The geometry of $\mathbb{R}$–covered foliations, Geom. Topol. 4 (2000) 457 MR1800151
12	D Calegari, Filling geodesics and hyperbolic complements, Geometry and the Imagination blog (2012)
13	J P Christy, Anosov flows on three-manifolds (topology, dynamics), PhD thesis, University of California, Berkeley (1984) MR2633722
14	Y Fang, Thermodynamic invariants of Anosov flows and rigidity, Discrete Contin. Dyn. Syst. 24 (2009) 1185 MR2505698
15	S R Fenley, Anosov flows in 3–manifolds, Ann. of Math. 139 (1994) 79 MR1259365
16	S R Fenley, Quasigeodesic Anosov flows and homotopic properties of flow lines, J. Differential Geom. 41 (1995) 479 MR1331975
17	S R Fenley, Foliations, topology and geometry of 3–manifolds: $\mathbb{R}$–covered foliations and transverse pseudo-Anosov flows, Comment. Math. Helv. 77 (2002) 415 MR1933786
18	S Fenley, Ideal boundaries of pseudo-Anosov flows and uniform convergence groups with connections and applications to large scale geometry, Geom. Topol. 16 (2012) 1 MR2872578
19	R Feres, A Katok, Invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows, Ergodic Theory Dynam. Systems 9 (1989) 427 MR1016661
20	P Foulon, Entropy rigidity of Anosov flows in dimension three, Ergodic Theory Dynam. Systems 21 (2001) 1101 MR1849603
21	P Foulon, B Hasselblatt, Zygmund strong foliations, Israel J. Math. 138 (2003) 157 MR2031955
22	J Franks, B Williams, Anomalous Anosov flows, from: "Global theory of dynamical systems" (editors Z Nitecki, C Robinson), Lecture Notes in Math. 819, Springer (1980) 158 MR591182
23	H Geiges, An introduction to contact topology, Cambridge Studies in Advanced Mathematics 109, Cambridge Univ. Press (2008) MR2397738
24	É Ghys, Flots d'Anosov sur les 3–variétés fibrées en cercles, Ergodic Theory Dynam. Systems 4 (1984) 67 MR758894
25	É Ghys, Flots d'Anosov dont les feuilletages stables sont différentiables, Ann. Sci. École Norm. Sup. 20 (1987) 251 MR911758
26	S Goodman, Dehn surgery on Anosov flows, from: "Geometric dynamics" (editor J Palis Jr.), Lecture Notes in Math. 1007, Springer (1983) 300 MR1691596
27	U Hamenstädt, Regularity of time-preserving conjugacies for contact Anosov flows with $C^1$–Anosov splitting, Ergodic Theory Dynam. Systems 13 (1993) 65 MR1213079
28	M Handel, W P Thurston, Anosov flows on new three manifolds, Invent. Math. 59 (1980) 95 MR577356
29	B Hasselblatt, Hyperbolic dynamical systems, from: "Handbook of dynamical systems 1A" (editors B Hasselblatt, A Katok), North-Holland (2002) 239 MR1928520
30	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
31	A Hatcher, Notes on basic 3–manifold topology (2007)
32	M W Hirsch, Differential topology, Graduate Texts in Mathematics 33, Springer (1976) MR0448362
33	H Hofer, Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993) 515 MR1244912
34	E Hopf, Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung, Ber. Verh. Sächs. Akad. Wiss. Leipzig 91 (1939) 261 MR0001464
35	S Hurder, A Katok, Differentiability, rigidity and Godbillon–Vey classes for Anosov flows, Inst. Hautes Études Sci. Publ. Math. (1990) 5 MR1087392
36	M Kanai, Geodesic flows of negatively curved manifolds with smooth stable and unstable foliations, Ergodic Theory Dynam. Systems 8 (1988) 215 MR951270
37	M Kapovich, Hyperbolic manifolds and discrete groups, Progress in Mathematics 183, Birkhäuser (2001) MR1792613
38	A Katok, B Hasselblatt, Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its Applications 54, Cambridge Univ. Press (1995) MR1326374
39	C Liverani, On contact Anosov flows, Ann. of Math. 159 (2004) 1275 MR2113022
40	J Martinet, Formes de contact sur les variétés de dimension $3$, from: "Proceedings of Liverpool Singularities Symposium II" (editor C T C Wall), Lecture Notes in Math. 209, Springer (1971) 142 MR0350771
41	D Matignon, Topologie en basse dimension: Remplissages de Dehn et théorie des n\oe uds, Habilitation à diriger des recherches, Université d’Aix-Marseille I (2004)
42	Y Mitsumatsu, Anosov flows and non-Stein symplectic manifolds, Ann. Inst. Fourier (Grenoble) 45 (1995) 1407 MR1370752
43	J P Otal, Le théorème d'hyperbolisation pour les variétés fibrées de dimension 3, Astérisque 235 (1996) MR1402300
44	C Petronio, J Porti, Negatively oriented ideal triangulations and a proof of Thurston's hyperbolic Dehn filling theorem, Expo. Math. 18 (2000) 1 MR1751141
45	J F Plante, Anosov flows, Amer. J. Math. 94 (1972) 729 MR0377930
46	J F Plante, W P Thurston, Anosov flows and the fundamental group, Topology 11 (1972) 147 MR0295389
47	P Scott, The geometries of 3–manifolds, Bull. London Math. Soc. 15 (1983) 401 MR705527
48	W P Thurston, Three-manifolds, foliations and circles I arXiv:math/9712268
49	W P Thurston, The geometry and topology of three-manifolds (1980)
50	W P Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. 6 (1982) 357 MR648524
51	P Tomter, Anosov flows on infra-homogeneous spaces, from: "Global analysis", Proc. Sympos. Pure Math. 14, Amer. Math. Soc. (1970) 299 MR0279831
52	F Waldhausen, Eine Klasse von 3–dimensionalen Mannigfaltigkeiten I, Invent. Math. 3 (1967) 308 MR0235576