Décomposition des difféomorphismes du tore en applications déviant la verticale (avec un appendice en collaboration avec Jean-Marc Gambaudo)

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1. [An1] S. B. ANGENENT. The periodic orbits of an area preserving twist map, Commun. Math. Phys., 115 (1988), 353-374. Zbl0665.58034MR89f:58118
2. [An2] S. B. ANGENENT. Monotone recurrence relations, their Birkhoff orbits and topological entropy, Ergod. Th. Dynam. Sys., 10 (1990), 15-41. Zbl0667.58036MR91b:58181
3. [AG] S. B. ANGENENT, C. GOLÉ. Lamination by ghost circles, preprint, E.T.H. Zurich, (1991). 
4. [Arno] V. I. ARNOLD. Méthodes mathématiques de la mécanique classique, Editions MIR. Zbl0385.70001
5. [Arna] M.-C. ARNAUD. Le "closing lemma" en topologie C1, Mémoires Soc. Math. France, 74 (1998). Zbl0920.58039MR99h:58097
6. [Ba] V. BANGERT. On the existence of closed geodesics on two-spheres, International. J. of Math., 4 (1993), 1-10. Zbl0791.53048MR94d:58036
7. [Bi] G. BIRKHOFF. Extensions of Jentzsch's theorem, Trans. Amer. Math. Soc., 85 (1957), 219-227. Zbl0079.13502MR19,296a
8. [Bi2] G. D. BIRKHOFF. An extension of Poincaré's last Geometric theorem, Acta Math., 47 (1925), 297-311. JFM52.0573.02
9. [Br] L. E. J. BROUWER. Beweis des ebenen Translationssatzes, Math. Ann., 72 (1912), 37-54. Zbl43.0569.02JFM43.0569.02
10. [BM] C. BAESENS, R. S. MAC KAY. Gradient dynamics of tilted Frenkel-Kontorova models, Nonlinearity, 11 (1998), 949-964. Zbl0906.58037MR99i:58134
11. [Ca] C. CARATHÉODORY. Untersuchungen űber die konforme Abbildungen von festen und ver$att$¨ãnderlichen Gebieten, Math. Ann., 72 (1912), 107-144. JFM43.0524.01
12. [Ce] J. CERF. Topologie de certains espaces de plongements, Bull. Soc. Math. France, 89 (1961), 227-380. Zbl0101.16001MR25 #3543
13. [Cha] M. CHAPERONUne idée du type "géodésiques brisées" pour les systèmes hamiltoniens, C. R. Acad. Sc. Paris, 298 (1984), 293-296. Zbl0576.58010MR86f:58049
14. [Che] YU. V. CHEKANOV. Critical points of quasifunctions and generating families of Legendrian manifolds, Funktsional. Anal. i Prilozhen, 30 (1996), 56-69. Zbl0873.58017MR97f:58016
15. [Co] C. CONLEY. Isolated invariant sets and the Morse index, Conference board of the Mathematical Sciences, 38 (1978). Zbl0397.34056MR80c:58009
16. [CE] C. CONLEY, R. EASTON. Isolated invariant sets and isolating blocks, Trans. Amer. Math. Soc., 158 (1971), 35-61. Zbl0223.58011MR43 #5551
17. [CZ] C. CONLEY, E. ZEHNDER. The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold, Invent. Math., 73 (1983), 33-49. Zbl0516.58017MR85e:58044
18. [Ep] D. EPSTEIN. Curves on 2-manifolds and isotopies, Acta. Math., 115 (1966), 83-107. Zbl0136.44605MR35 #4938
19. [EE] C. EARLE, J. EELLS. A fibre bundle description of teichműller theory, J. Diff. Geom., 4 (1970), 169-185. Zbl0185.32901
20. [FLP] A. FATHI, F. LAUDENBACH, V. POENARU. Travaux de Thurston sur les surfaces, Astérisque, Soc. Math. France, 66-67 (1979), 621-626. Zbl0406.00016MR82m:57003
21. [Flo] A. FLOER. A refinement of Conley index and an application to the stability of hyperbolic invariant sets. Ergod. Th. Dynam. Sys., 7 (1987), 93-103. Zbl0633.58040MR88g:58143
22. [Flu] M. FLUCHER. Fixed points of measure preserving homeomorphisms, Manuscripta Math., 68 (1990), 271-293. Zbl0722.58027MR91j:58129
23. [Fr1] J. FRANKS. Generalizations of the Poincaré-Birkhoff theorem, Annals of Math., 128 (1988), 139-151. Zbl0676.58037MR89m:54052
24. [Fr2] J. FRANKS. A variation on the Poincaré-Birkhoff Theorem, Contemp. Math., 81 (1988), 139-151. Zbl0676.58037MR90e:58095
25. [Fr3] J. FRANKS. Geodesics on S2 and periodic points of annulus homeomorphisms, Invent. Math., 108 (1992), 403-418. Zbl0766.53037MR93f:58192
26. [Fr4] J. FRANKS. Area preserving homeomorphisms of open surfaces of genus zero, New York J. Math., 2 (1996), 1-19. Zbl0891.58033MR97c:58123
27. [GL] J.-M. GAMBAUDO, P. LE CALVEZ. Infinité d'orbites périodiques pour les homéomorphismes conservatifs de l'anneau, ce volume. 
28. [Go] C. GolÉ. Ghost circles for twist maps, J. Diff. Equations, 97 (1992), 140-173. Zbl0777.58035MR93h:58115
29. [Gr] A. GRAMAIN, Le type d'homotopie du groupe des difféomorphismes d'une surface, Ann. Scient. Ec. Norm. Sup., 6 (1973), 53-66. Zbl0265.58002MR48 #5116
30. [Gu] L. GUILLOU. Théorème de translation plane de Brouwer et généralisations du théorème de Poincaré-Birkhoff, Topology, 33 (1990), 331-351. Zbl0924.55001MR95h:55003
31. [Ha] M. HAMSTROM. Homotopy groups of the space of homeomorphisms on a 2-manifold. Illinois J. Math.,.10 (1966), 563-573. Zbl0151.33002MR34 #2014
32. [HZ] H. HOFER, E. ZEHNDER. Symplectic invariants and Hamiltonian dynamics, Birkhaüser, Basel, Boston, Berlin, (1994). Zbl0805.58003MR96g:58001
33. [K] B. DE KÉRÉKJÁRTÓ. The plane translation theorem of Brouwer and the last geometric theorem of Poincaré, Acta Sci. Math. Szeged, 4 (1928-1929), 86-102. Zbl54.0612.02JFM54.0612.02
34. [L] P. LE CALVEZ. Décomposition des difféomorphismes du tore en applications déviant la verticale, ce volume. 
35. [L1] P. LE CALVEZ. Propriétés dynamiques de l'anneau et du tore, Astérisque, Soc. Math. France, 204 (1991). Zbl0784.58033MR94d:58092
36. [L2] P. LE CALVEZ. Une généralisation du théorème de Conley-Zehnder au tore de dimension 2, Ergod. Th. Dynam. Syst., 17 (1997), 71-80. Zbl0877.58011MR98j:58093
37. [L3] P. LE CALVEZ. Construction d'orbites périodiques par perturbation d'un difféomorphisme de l'anneau déviant la verticale, C.R. Acad. Sci. Paris, 321 (1995), 463-468. Zbl0854.57023MR96h:58144
38. [LM] R. LUKE, W. MASON. The space of homeomorphisms on a compact 2-manifold is an A.N.R., Trans. Amer. Math. Soc., 164 (1972), 275-285. Zbl0235.57002MR46 #849
39. [MS] R. MAC KAY, J. STARCK. Lectures on orbits of minimal action for area-presering maps, preprint, University of Warwick, (1985). 
40. [Ma] J. N. MATHER. Amount of rotation about a point and the Morse index, Commun. Math. Phys., 21 (1982), 457-467. MR84g:58084
41. [Mo] P. VAN MORBEKE. The spectrum of Jacobi Matrices, Inventiones math., 37 (1976), 45-81. Zbl0361.15010MR58 #31226
42. [PR] C. PUGH, C. ROBINSON. The closing lemma including Hamiltonians Ergod. Th. Dynam. Sys. 3 (1983), 261-313 Zbl0548.58012MR85m:58106
43. [Ra] T. RADO. Sur la représentation conforme des domaines variables, Acta. Sci. Math. Szeged, 1 (1923), 180-186. Zbl49.0247.03JFM49.0247.03
44. [Ru] D. RUELLE. Analycity properties of the characteristic exponents of random matrix products, Adv. in Math, 32 (1979), 68-80. Zbl0426.58018MR80e:58035
45. [S] S. SCHWARTZMAN. Asymptotic cycles. Ann. of Maths, 68 (1957), 270-284. Zbl0207.22603MR19,568i
46. [Sh] M. SHUB. Stabilité globale des systèmes dynamiques, Astérisque, Soc. Math. France, 56 (1978). Zbl0396.58014MR80c:58015
47. [Si] J.-C. SIKORAV. Problème d'intersection et de points fixes en géométrie hamiltonienne, Comm. Math. Helvet., 62 (1987), 62-73. Zbl0684.58015MR88g:58067
48. [Sm] S. SMALE. Diffeomorphisms of the 2-sphere, Proc. Amer. Math. Soc., 10 (1959), 621-626. Zbl0118.39103MR22 #3004
49. [T] W. P. THURSTON. On the geometry and dynamic of diffeomorphisms of surfaces, Bull. Amer. Math. Soc., 19 (1988), 417-431. Zbl0674.57008MR89k:57023
50. [V] C. VITERBO. Symplectic topology as the geometry of generating functions, Math. Ann., 292 (1992), 685-710. Zbl0735.58019MR93b:58058
51. [Wh] H. WHITNEY. Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc., 36 (1934), 63-89. Zbl0008.24902MR1501735JFM60.0217.01
52. [Wi] H. E. WINLELNKEMPER. Twist maps, covering and Brouwer's translation theorem, Trans. Amer. Math. Soc., 267 (1981), 585-593. Zbl0474.58015MR84c:58069

1. Patrice Le Calvez, Pourquoi les points périodiques des homéomorphismes du plan tournent-ils autour de certains points fixes ?