Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension 3
Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 786, 25 p.
@incollection{SB_1993-1994__36__309_0,
     author = {Laudenbach, Fran\c{c}ois},
     title = {Orbites p\'eriodiques et courbes pseudo-holomorphes. {Application} \`a la conjecture de {Weinstein} en dimension $3$},
     booktitle = {S\'eminaire Bourbaki : volume 1993/94, expos\'es 775-789},
     series = {Ast\'erisque},
     note = {talk:786},
     pages = {309--333},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {227},
     year = {1995},
     mrnumber = {1321652},
     zbl = {0853.57013},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1993-1994__36__309_0/}
}
TY  - CHAP
AU  - Laudenbach, François
TI  - Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension $3$
BT  - Séminaire Bourbaki : volume 1993/94, exposés 775-789
AU  - Collectif
T3  - Astérisque
N1  - talk:786
PY  - 1995
SP  - 309
EP  - 333
IS  - 227
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/SB_1993-1994__36__309_0/
LA  - fr
ID  - SB_1993-1994__36__309_0
ER  - 
%0 Book Section
%A Laudenbach, François
%T Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension $3$
%B Séminaire Bourbaki : volume 1993/94, exposés 775-789
%A Collectif
%S Astérisque
%Z talk:786
%D 1995
%P 309-333
%N 227
%I Société mathématique de France
%U http://www.numdam.org/item/SB_1993-1994__36__309_0/
%G fr
%F SB_1993-1994__36__309_0
Laudenbach, François. Orbites périodiques et courbes pseudo-holomorphes. Application à la conjecture de Weinstein en dimension $3$, dans Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 786, 25 p. http://www.numdam.org/item/SB_1993-1994__36__309_0/

[AL] M. Audin, J. Lafontaine, eds., Holomorphic curves in symplectic geometry, Birkhäuser, 1994. | MR | Zbl

[Be1] D. Bennequin, Entrelacements et équations de Pfaff, Astérisque 103-108 (1983), 83-161. | Numdam | MR | Zbl

[Be2] D. Bennequin, Caustique mystique [d'après Arnold et al.], Sém. Bourbaki, Astérisque 133-134 (1986), 19-56. | EuDML | Numdam | MR | Zbl

[Be3] D. Bennequin, Problèmes elliptiques, surfaces de Riemann et structures symplectiques [d'après M. Gromov], Sém. Bourbaki, Astérisque 145- 146 (1987), 111-136. | EuDML | Numdam | MR | Zbl

[BG] E. Bedford, B. Gaveau, Envelopes of holomorphy of certain 2 -spheres in 𝐂 2 , Amer. J. of Math. 105 (1983), 975-1009. | DOI | MR | Zbl

[Ber] H. Berestycki, Solutions périodiques de systèmes hamiltoniens, Sém. Bourbaki, Astérisque 105-106 (1983), 105-128. | EuDML | Numdam | MR | Zbl

[Bers] L. Bers, An outline of the theory of pseudo-analytic functions, Bull. Amer. Math. Soc. 62 (1956), 291-331. | MR | Zbl

[Bi] E. Bishop, Differentiable manifolds in complex Euclidian space, Duke Math. J. | MR | Zbl

[El1] Y. Eliashberg, Classification of overtwisted contact structures on 3- manifolds, Invent. Math. 98 (1989), 623-637. | MR | Zbl

[El2] Y. Eliashberg, Filling by holomorphic discs and its applications, London Math. Soc. Lect. Notes Ser. 151 (1991), 45-67. | MR | Zbl

[El3] Y. Eliashberg, Contact 3-manifolds, twenty years since J. Martinet's work, Ann. Inst. Fourier 42 (1992), 165-192. | Numdam | MR | Zbl

[Ga] P. Gauduchon, The canonical almost complex structure on the manifold of 1-jets of pseudo-holomorphic mappings between two almost complex manidolds, p. 69-74 in [AL].

[Gi1] E. Giroux, Convexité en topologie de contact, Comment. Math. Helv. 66 (1991), 637-677. | MR | Zbl

[Gi2] E. Giroux, Topologie de contact en dimension trois [autour de travaux de Yakov Eliashberg], Sém. Bourbaki, Astérisque 216 (1993), 7-34. | Numdam | MR | Zbl

[Gr] M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. math. 82 (1985), 307-347. | MR | Zbl

[Hed] G. Hedlund, Fuchsian groups and transitive horocycles, Duke Math. Journal 2 (1936), 530-542. | JFM | MR

[Hem] J. Hempel, 3-manifolds, Annals of Math. Studies, Princeton Univ. Press, 1976. | MR | Zbl

[Her] M. Herman, Exemples de flots hamiltoniens dont aucune perturbation en topologie C n'a d'orbites périodiques sur un ouvert de surfaces d'énergie, C. R. Acad. Sc. Paris série I Math. 312 (1991), 989-994. | Zbl

[Ho] H. Hofer, Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three, Invent. Math. 114 (1993), 515-563. | MR | Zbl

[HV] H. Hofer, C. Viterbo, The Weinstein conjecture in the presence of holomorphic spheres, Comm. Pure Appl. Math. 45 (1992), 583-622. | MR | Zbl

[HW] H. Hofer, K. Wysocki, communication orale.

[Lab] F. Labourie, communication orale.

[LF] L. Lusternik, A. Fet, Variational problems on closed manifolds, Dokl. Akad. Nauk SSSR 81 (1951), 17-18. | MR | Zbl

[Ma] J. Martinet, Formes de contact sur les variétés de dimension trois, p. 142-163 in Proceedings of Liverpool Singularities Symposium II, L.N.M. 209, Springer, 1971. | MR | Zbl

[Mc1] D. Mcduff, The structure of rational and ruled symplectic 4-manifolds, J. of AMS 3 (1990), 672-712. | MR | Zbl

[Mc2] D. Mcduff, The local behaviour of holomorphic curves in almost complex 4-manifolds, J. of Diff. Geo. 34 (1991), 143-164. | MR | Zbl

[Mc3] D. Mcduff, Symplectic manifolds with contact type boundaries, Invent. math. 103 (1991), 651-671. | MR | Zbl

[Mc4] D. Mcduff, Singularities and positivity of intersections of J-holomorphic curves, p. 191-215 in [AL]. | MR

[Mi] J. Milnor, On the 3 -dimensional Brieskorn manifolds M ( p , q , r ) , p. 175-225 in : Knots, groups and 3 -manifolds, (papers dedicated to the memory of R.H. Fox, ed. by L. Neuwirth, Annals of Math. Studies 84, Princeton Univ. Press, 1975. | MR | Zbl

[Mu] M.-P. Muller, Gromov's Schwarz lemma as an estimate of the gradient for holomorphic curves, p. 217-231 in [AL]. | MR

[MW] M. Micallef, B. White, The structure of branch points in minimal surfaces and pseudoholomorphic curves, preprint 1994.

[Pa] P. Pansu, Compactness, p. 233-249 in [AL]. | MR

[Ra] P. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978), 157-184. | DOI | MR | Zbl

[Si] J.-C. Sikorav, Some properties of holomorphic curves in almost complex manifolds, p. 165-189 in [AL]. | MR

[SU] J. Sacks, K. Uhlenbeck, The existence of minimal immersions of two spheres, Ann. of Math. 113 (1981), 1-24. | DOI | MR | Zbl

[Ve] I. N. Vekua, Generalized analytical functions, Pergamon, London, 1962. | MR

[Vi] C. Viterbo, A proof of the Weinstein conjecture in 𝐑 2 n , Ann. Inst. Henri Poincaré, Analyse non linéaire 4 (1987), 337-357. | DOI | EuDML | Numdam | MR | Zbl

[We] A. Weinstein, On the hypotheses of Rabinowitz's periodic orbit theorems, J. Diff. Eq. 33 (1979), 353-358. | DOI | MR | Zbl