According to Lemma 10.3 and 10.4, ? k is a strongly transverse gluing diffeomorphism. Now consider the closed manifold M k := (W + ? W ? )/? k and the vector field Z k on M k induced by the vector fields Z and ?Z (more precisely, Z k := Z on W + and Z k := ?Z on W ? ) According to Theorem 1.5, up to modifying Z by a topological equivalence and ? k by a strongly transverse isotopy, Z k is an Anosov vector field. Since the gluing map ? k is isotopic to the identity for every k, the manifolds M 1, M n with a single manifold M , and see Z 1 , . . . , Z n as vector fields on this manifold M ,
Caractérisation des flots d'Anosov en dimension 3 par leurs feuilletages faibles, Ergodic Theory Dynam, Systems, vol.15, pp.247-270, 1995. ,
DOI : 10.1017/s0143385700008361
Flots d'Anosov sur les vari??t??s graph??es au sens de Waldhausen, Annales de l???institut Fourier, vol.46, issue.5, pp.1451-1517, 1996. ,
DOI : 10.5802/aif.1556
URL : http://archive.numdam.org/article/AIF_1996__46_5_1451_0.pdf
Mise en position optimale de tores par rapport ?? un flot d'Anosov, Commentarii Mathematici Helvetici, vol.70, issue.1, pp.113-160, 1995. ,
DOI : 10.1007/BF02566001
Generalizations of the Bonatti???Langevin example of Anosov flow and their classification up to topological equivalence, Communications in Analysis and Geometry, vol.6, issue.4, pp.749-798, 1998. ,
DOI : 10.4310/CAG.1998.v6.n4.a5
Pseudo-Anosov flows in toroidal manifolds, Geom. Topol, vol.17, issue.4, pp.1877-1954, 2013. ,
Flots de Smale en dimension 3: pr??sentations finies de voisinages invariants d'ensembles selles, Topology, vol.41, issue.1, pp.119-162, 2002. ,
DOI : 10.1016/S0040-9383(00)00032-X
A spectral-like decomposition for transitive Anosov flows in dimension three, preparing ,
Un exemple de flot d'Anosov transitif transverse un tore et non conjuguéconjuguéà une suspension. (French) [An example of a transitive Anosov flow transversal to a torus and not conjugate to a suspension] Ergodic Theory Dynam, Systems, vol.14, issue.4, pp.633-643, 1994. ,
DOI : 10.1017/s0143385700008099
Separating the basic sets of a nontransitive Anosov flow, Bull. London Math. Soc, vol.25, issue.5, pp.487-490, 1993. ,
Anosov Flows on Three Manifolds, 1984. ,
Branched surfaces and attractors. I. Dynamic branched surfaces, Trans. Amer. Math. Soc, vol.336, issue.2, pp.759-784, 1993. ,
DOI : 10.2307/2154374
Anosov Flows in 3-Manifolds, The Annals of Mathematics, vol.139, issue.1, pp.79-115, 1994. ,
DOI : 10.2307/2946628
The structure of branching in Anosov flows of 3-manifolds, Commentarii Mathematici Helvetici, vol.73, issue.2, pp.259-297, 1998. ,
DOI : 10.1007/s000140050055
Anomalous Anosov flows. Global theory of dynamical systems, Proc. Internat. Conf., Northwestern Univ. Lecture Notes in Math, vol.819, pp.158-174, 1979. ,
Transitive Anosov flows and pseudo-Anosov maps, Topology, vol.22, issue.3, pp.299-303, 1983. ,
Knots and Links in Three-dimension Flows, Lectures Notes in Mathematics, 1654. ,
Flots d'Anosov sur les 3-variéts fibrées en cercles, Ergodic Theory Dynam. Systems, vol.4, issue.1, pp.67-80, 1984. ,
Flots d'Anosov dont les feuilletages stables sont diff??rentiables, Annales scientifiques de l'??cole normale sup??rieure, vol.20, issue.2 ,
DOI : 10.24033/asens.1532
URL : http://archive.numdam.org/article/ASENS_1987_4_20_2_251_0.pdf
Hyperbolic nonwandering sets on two, Dynamical Systems, pp.293-301, 1973. ,
Anosov Flows, Transversely Affine Foliations, and a Conjecture of Verjovsky, Journal of the London Mathematical Society, vol.2, issue.2, pp.359-362, 1981. ,
DOI : 10.1112/jlms/s2-23.2.359
Differentiable dynamical systems, Bull. Amer. Math. Soc, vol.73, pp.747-817, 1967. ,
Hyperbolic structures on 3 -manifolds, II: Surface groups and 3- manifolds which fiber over the circle ,
93430 Villetaneuse, FRANCE E-mail: beguin@math.univ-paris13.fr Christian Bonattimail : bonatti@u-bourgogne, p.92, 2000. ,