Décomposition des difféomorphismes du tore en applications déviant la verticale (avec un appendice en collaboration avec Jean-Marc Gambaudo) (1999)


Le Calvez, Patrice
Mémoires de la Société Mathématique de France, Tome 79 (1999) v-146 p doi : 10.24033/msmf.392
URL stable : http://www.numdam.org/item?id=MSMF_1999_2_79__R3_0

Bibliographie

[An1] S. B. Angenent. The periodic orbits of an area preserving twist map, Commun. Math. Phys., 115 (1988), 353-374. MR 89f:58118 | Zbl 0665.58034

[An2] S. B. Angenent. Monotone recurrence relations, their Birkhoff orbits and topological entropy, Ergod. Th. Dynam. Sys., 10 (1990), 15-41. MR 91b:58181 | Zbl 0667.58036

[AG] S. B. Angenent, C. Golé. Lamination by ghost circles, preprint, E.T.H. Zurich, (1991).

[Arno] V. I. Arnold. Méthodes mathématiques de la mécanique classique, Editions MIR. Zbl 0385.70001

[Arna] M.-C. Arnaud. Le "closing lemma" en topologie C1, Mémoires Soc. Math. France, 74 (1998). Numdam | MR 99h:58097 | Zbl 0920.58039

[Ba] V. Bangert. On the existence of closed geodesics on two-spheres, International. J. of Math., 4 (1993), 1-10. MR 94d:58036 | Zbl 0791.53048

[Bi] G. Birkhoff. Extensions of Jentzsch's theorem, Trans. Amer. Math. Soc., 85 (1957), 219-227. MR 19,296a | Zbl 0079.13502

[Bi2] G. D. Birkhoff. An extension of Poincaré's last Geometric theorem, Acta Math., 47 (1925), 297-311. JFM 52.0573.02

[Br] L. E. J. Brouwer. Beweis des ebenen Translationssatzes, Math. Ann., 72 (1912), 37-54. JFM 43.0569.02

[BM] C. Baesens, R. S. Mac Kay. Gradient dynamics of tilted Frenkel-Kontorova models, Nonlinearity, 11 (1998), 949-964. MR 99i:58134 | Zbl 0906.58037

[Ca] C. Carathéodory. Untersuchungen űber die konforme Abbildungen von festen und veratt¨ãnderlichen Gebieten, Math. Ann., 72 (1912), 107-144. JFM 43.0524.01

[Ce] J. Cerf. Topologie de certains espaces de plongements, Bull. Soc. Math. France, 89 (1961), 227-380. Numdam | MR 25 #3543 | Zbl 0101.16001

[Cha] M. Chaperon Une idée du type "géodésiques brisées" pour les systèmes hamiltoniens, C. R. Acad. Sc. Paris, 298 (1984), 293-296. MR 86f:58049 | Zbl 0576.58010

[Che] Yu. V. Chekanov. Critical points of quasifunctions and generating families of Legendrian manifolds, Funktsional. Anal. i Prilozhen, 30 (1996), 56-69. MR 97f:58016 | Zbl 0873.58017

[Co] C. Conley. Isolated invariant sets and the Morse index, Conference board of the Mathematical Sciences, 38 (1978). MR 80c:58009 | Zbl 0397.34056

[CE] C. Conley, R. Easton. Isolated invariant sets and isolating blocks, Trans. Amer. Math. Soc., 158 (1971), 35-61. MR 43 #5551 | Zbl 0223.58011

[CZ] C. Conley, E. Zehnder. The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold, Invent. Math., 73 (1983), 33-49. MR 85e:58044 | Zbl 0516.58017

[Ep] D. Epstein. Curves on 2-manifolds and isotopies, Acta. Math., 115 (1966), 83-107. MR 35 #4938 | Zbl 0136.44605

[EE] C. Earle, J. Eells. A fibre bundle description of teichműller theory, J. Diff. Geom., 4 (1970), 169-185. Zbl 0185.32901

[FLP] A. Fathi, F. Laudenbach, V. Poenaru. Travaux de Thurston sur les surfaces, Astérisque, Soc. Math. France, 66-67 (1979), 621-626. MR 82m:57003 | Zbl 0406.00016

[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. MR 88g:58143 | Zbl 0633.58040

[Flu] M. Flucher. Fixed points of measure preserving homeomorphisms, Manuscripta Math., 68 (1990), 271-293. MR 91j:58129 | Zbl 0722.58027

[Fr1] J. Franks. Generalizations of the Poincaré-Birkhoff theorem, Annals of Math., 128 (1988), 139-151. MR 89m:54052 | Zbl 0676.58037

[Fr2] J. Franks. A variation on the Poincaré-Birkhoff Theorem, Contemp. Math., 81 (1988), 139-151. MR 90e:58095 | Zbl 0676.58037

[Fr3] J. Franks. Geodesics on S2 and periodic points of annulus homeomorphisms, Invent. Math., 108 (1992), 403-418. MR 93f:58192 | Zbl 0766.53037

[Fr4] J. Franks. Area preserving homeomorphisms of open surfaces of genus zero, New York J. Math., 2 (1996), 1-19. MR 97c:58123 | Zbl 0891.58033

[GL] J.-M. Gambaudo, P. Le Calvez. Infinité d'orbites périodiques pour les homéomorphismes conservatifs de l'anneau, ce volume.

[Go] C. Golé. Ghost circles for twist maps, J. Diff. Equations, 97 (1992), 140-173. MR 93h:58115 | Zbl 0777.58035

[Gr] A. Gramain, Le type d'homotopie du groupe des difféomorphismes d'une surface, Ann. Scient. Ec. Norm. Sup., 6 (1973), 53-66. Numdam | MR 48 #5116 | Zbl 0265.58002

[Gu] L. Guillou. Théorème de translation plane de Brouwer et généralisations du théorème de Poincaré-Birkhoff, Topology, 33 (1990), 331-351. MR 95h:55003 | Zbl 0924.55001

[Ha] M. Hamstrom. Homotopy groups of the space of homeomorphisms on a 2-manifold. Illinois J. Math.,.10 (1966), 563-573. MR 34 #2014 | Zbl 0151.33002

[HZ] H. Hofer, E. Zehnder. Symplectic invariants and Hamiltonian dynamics, Birkhaüser, Basel, Boston, Berlin, (1994). MR 96g:58001 | Zbl 0805.58003

[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. JFM 54.0612.02

[L] P. Le Calvez. Décomposition des difféomorphismes du tore en applications déviant la verticale, ce volume.

[L1] P. Le Calvez. Propriétés dynamiques de l'anneau et du tore, Astérisque, Soc. Math. France, 204 (1991). MR 94d:58092 | Zbl 0784.58033

[L2] P. Le Calvez. Une généralisation du théorème de Conley-Zehnder au tore de dimension 2, Ergod. Th. Dynam. Syst., 17 (1997), 71-80. MR 98j:58093 | Zbl 0877.58011

[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. MR 96h:58144 | Zbl 0854.57023

[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. MR 46 #849 | Zbl 0235.57002

[MS] R. Mac Kay, J. Starck. Lectures on orbits of minimal action for area-presering maps, preprint, University of Warwick, (1985).

[Ma] J. N. Mather. Amount of rotation about a point and the Morse index, Commun. Math. Phys., 21 (1982), 457-467. MR 84g:58084

[Mo] P. Van Morbeke. The spectrum of Jacobi Matrices, Inventiones math., 37 (1976), 45-81. MR 58 #31226 | Zbl 0361.15010

[PR] C. Pugh, C. Robinson. The closing lemma including Hamiltonians Ergod. Th. Dynam. Sys. 3 (1983), 261-313 MR 85m:58106 | Zbl 0548.58012

[Ra] T. Rado. Sur la représentation conforme des domaines variables, Acta. Sci. Math. Szeged, 1 (1923), 180-186. JFM 49.0247.03

[Ru] D. Ruelle. Analycity properties of the characteristic exponents of random matrix products, Adv. in Math, 32 (1979), 68-80. MR 80e:58035 | Zbl 0426.58018

[S] S. Schwartzman. Asymptotic cycles. Ann. of Maths, 68 (1957), 270-284. MR 19,568i | Zbl 0207.22603

[Sh] M. Shub. Stabilité globale des systèmes dynamiques, Astérisque, Soc. Math. France, 56 (1978). MR 80c:58015 | Zbl 0396.58014

[Si] J.-C. Sikorav. Problème d'intersection et de points fixes en géométrie hamiltonienne, Comm. Math. Helvet., 62 (1987), 62-73. MR 88g:58067 | Zbl 0684.58015

[Sm] S. Smale. Diffeomorphisms of the 2-sphere, Proc. Amer. Math. Soc., 10 (1959), 621-626. MR 22 #3004 | Zbl 0118.39103

[T] W. P. Thurston. On the geometry and dynamic of diffeomorphisms of surfaces, Bull. Amer. Math. Soc., 19 (1988), 417-431. MR 89k:57023 | Zbl 0674.57008

[V] C. Viterbo. Symplectic topology as the geometry of generating functions, Math. Ann., 292 (1992), 685-710. MR 93b:58058 | Zbl 0735.58019

[Wh] H. Whitney. Analytic extensions of differentiable functions defined in closed sets. Trans. Amer. Math. Soc., 36 (1934), 63-89. JFM 60.0217.01 | MR 1501735 | Zbl 0008.24902

[Wi] H. E. Winlelnkemper. Twist maps, covering and Brouwer's translation theorem, Trans. Amer. Math. Soc., 267 (1981), 585-593. MR 84c:58069 | Zbl 0474.58015