Propriétés dynamiques des difféomorphismes de l'anneau et du tore
Astérisque, no. 204 (1991) , 133 p.

Voir la notice du livre provenant de la source

MR   Zbl

Le Calvez, Patrice. Propriétés dynamiques des difféomorphismes de l'anneau et du tore. Astérisque, no. 204 (1991), 133 p. http://geodesic.mathdoc.fr/item/AST_1991__204__1_0/
@book{AST_1991__204__1_0,
     author = {Le Calvez, Patrice},
     title = {Propri\'et\'es dynamiques des diff\'eomorphismes de l'anneau et du tore},
     series = {Ast\'erisque},
     year = {1991},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {204},
     mrnumber = {1183304},
     zbl = {0784.58033},
     language = {fr},
     url = {http://geodesic.mathdoc.fr/item/AST_1991__204__1_0/}
}
TY  - BOOK
AU  - Le Calvez, Patrice
TI  - Propriétés dynamiques des difféomorphismes de l'anneau et du tore
T3  - Astérisque
PY  - 1991
IS  - 204
PB  - Société mathématique de France
UR  - http://geodesic.mathdoc.fr/item/AST_1991__204__1_0/
LA  - fr
ID  - AST_1991__204__1_0
ER  - 
%0 Book
%A Le Calvez, Patrice
%T Propriétés dynamiques des difféomorphismes de l'anneau et du tore
%S Astérisque
%D 1991
%N 204
%I Société mathématique de France
%U http://geodesic.mathdoc.fr/item/AST_1991__204__1_0/
%G fr
%F AST_1991__204__1_0

[AY] K. Alligood, J. Yorke. Cascades of period-doubling bifurcations: a prerequisite for horseshoes, Bull. Amer. Math. Soc., 9 (1983), 319-322. | MR | Zbl | DOI

[An] S. B. Angenent. Monotone recurrence relations, their Birkhoff orbits and topological entropy, Ergod. Th. Dynam. Sys., 10 (1990), 15-41. | MR | Zbl | DOI

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

[AL] S. Aubry, P. Y. Le Daeron. The discrete Frenkel-Kontorova model and its generalizations, Physica 8D(1983), 381-422. | Zbl

[Ba1] V. Bangert. Mather sets for twist maps and geodesics on tori, Dynamics reported, Vol I, 1988, John Wiley and Sons. | MR | Zbl | DOI

[Ba2] V. Bangert. Minimal geodesics, Ergod. Th. Dynam. Sys., 10 (1989), 263-286. | MR | Zbl

[BS] M. Barge, R. Swanson. Rotation shadowing properties of circle and annulus maps, Ergod. Th. Dynam. Sys., 8 (1988), 509-521. | MR | Zbl | DOI

[BG] M. Barge, R. M. Gillette. Rotation and periodicity in plane separating continua, preprint, Montana State University. | MR | Zbl | DOI

[BC] M. Benedicks, L. Carleson. The dynamics of the Hénon map, Ann. of Math., 133 (1991), 73-169. | MR | Zbl | DOI

[Be] D. Bernstein. Birkhoff periodic orbits for twist maps with the circle intersection property, Ergod. Th. Dynam. Sys., 5 (1985), 531-537. | MR | Zbl | DOI

[BK] D. Bernstein, A. Katok. Birkhoff periodic orbits for small perturbations of completely integrable Hamiltonian systems with convex Hamiltonians, Invent. Math., 88 (1987), 225-241. | MR | Zbl | EuDML | DOI

[Bi1] G. D. Birkhoff. Proof of Poincaré's last geometric theorem, Trans. Amer. Math. Soc., 14 (1913), 14-22 | MR | JFM

G. D. Birkhoff. Proof of Poincaré's last geometric theorem, Collected Math. Papers, vol I, 673-681, Dover, New-York, (1978).

[Bi2] G. D. Birkhoff. Surface transformation and their dynamical applications. Acta Math., 43 (1920), 1-119 ; et Collected Math. Papers, vol II, 111-229. | JFM | MR | DOI

[Bi3] G. D. Birkhoff. An extension of Poincaré's last geometric theorem, Acta Math., 47 (1926), 297-311 ; et Collected. Math. Papers vol II, 252-260. | MR | JFM | DOI

[Bi4] G. D. Birkhoff. On the periodic motions of dynamical systems, Acta. Math., 50 (1927), 359-379 ; et Collected Math. Papers, vol II, 333-353. | MR | JFM | DOI

[Bi5] G. D. Birkhoff. Sur quelques courbes fermées remarquables, Bull. Soc. Math. France, 80 (1932), 1-26 ; et Collected Math. Papers, vol II, 444-461. | MR | Zbl | JFM | Numdam | EuDML

[Bi6] G. D. Birkhoff. Sur l'existence de régions d'instabilité en dynamique, Ann. Inst. Henri Poincaré, 8, (1932) ; et Collected Math. Papers, vol II, 418-443. | Zbl | MR | JFM | EuDML | Numdam

[Bi7] G. D. Birkhoff. Nouvelles recherches sur les systèmes dynamiques, Memoriae Pont. Acad. Sci. Novi Lyncaei, 1 (1935), 85-216 ; et Collected Math. Papers, vol II, 530-661. | Zbl | JFM

[BGMY] L. Block, J. Guckenheimer, J. Misiurewicz, L. S. Young. Periodic points and topological entropy of one dimensional maps, L. N. in Math., 819, Springer Verlag, (1980), 18-34. | MR | Zbl

[Bo1] P. L. Boyland. Braid Types and a topological method of proving positive entropy, preprint.

[Bo2] P. L. Boyland. Rotations sets and Morse decomposition in twist maps, Ergod. Th. Dynam. Sys., 8 (1988), 33-61. | MR | Zbl | DOI

[Bo3] P. L. Boyland. Rotation sets and topologically monotone orbits for annulus homeo-morphisms, preprint, Univ. of Minessota.

[BH] P. L. Boyland, G. R. Hall. Invariant circles and the order structure of periodic orbits in monotone twist maps, Topology, 26 (1987), 21-35. | MR | Zbl | DOI

[Bw] R. Bowen. Entropy and the fundamental group, L. N. in Math. 668, Springer Verlag, (1978), 21-29. | MR | Zbl

[BF] R. Bowen, J. Franks. The periodic points of maps of the disk and the interval, Topology, 15 (1976), 337-342. | MR | Zbl | DOI

[Bwr] L. E. J. Brouwer. Beweis des ebenen Translationssatzes, Math. Ann., 72 (1912), 37-54. | MR | JFM | EuDML | DOI

[Br] M. Brown. A new proof of Brouwer's lemma on translation arcs, Houston J. of Math., 10 (1984), 35-41. | MR | Zbl

[BN] M. Brown, W. D. Neumann. Proof of the Poincaré-Birkhoff fixed point theorem, Mich. Math. J., 24 (1977), 21-31. | MR | Zbl | DOI

[By] M.-L. Byalyi. Aubry-Mather sets and Birkhoff s theorem for geodesic flows on a two-dimensional torus, preprint, Weizmann Inst., (1988). | MR | Zbl

[Cr] P. H. Carter. An improvement of the Poincaré-Birkhoff theorem, Trans. Amer. Math. Soc., 269 (1982), 285-299. | MR | Zbl

[CL] M. L. Cartwright, J. E. Littlewood. On non-linear differential equations of the second order : I. The equation ÿ-k(1-y 2 )+y=bkcos(λt+α),k large, J. London Math. Soc., 20 (1945), 180-189. | Zbl | MR | DOI

[Ci1] M. Casdagli. Periodic orbits for dissipative twist maps, Ergod. Th. Dynam. Sys., 7 (1987), 165-173. | MR | Zbl | DOI

[Ci2] M. Casdagli. Rotational chaos in dissipative systems, Physica 29D (1988), 365-386. | MR | Zbl

[CB] A. J. Casson, S. A. Bleiler, Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Students Texts, 9 (1988). | MR | Zbl

[Chp1] M. Chaperon, Une idée de "géodésiques brisées" pour les systèmes hamiltoniens, C. R. Acad. Sc. Paris, 298 (1984), 293-296. | MR | Zbl

[Chp2] M. Chaperon. An elementary proof of the Conley-Zehnder theorem, L. N. in Math., 1125 (1985), 1-8. | MR | Zbl

[Chr1] M. Charpentier. Sur quelques propriétés des courbes de M. Birkhoff, Bull. Soc. Math. France, 62 (1934), 193-224. | MR | Zbl | EuDML | Numdam | DOI

[Chr2] M. Charpentier. Sur des courbes fermées analogues aux courbes de M. Birkhoff, J. Math. Pures et Appl., 14 (1935), 1-48. | Zbl | JFM | Numdam

[Che1] A. Chenciner. Sur un énoncé dissipatif du théorème géométrique de Poincaré-Birkhoff, C. R. Acad. Sc. Paris, 294 (1982), 243-246. | MR | Zbl

[Che2] A. Chenciner. La dynamique au voisinage d'un point fixe elliptique conservatif : de Poincaré et Birkhoff à Aubry et Mather, Séminaire Bourbaki, 622, Astérisque, Soc. Math. France, (1985), 165-173. | Zbl | MR | EuDML | Numdam

[CGT] A. Chenciner, J. M. Gambaudo, C. Tresser. Une remarque sur la structure des endomorphismes de degré 1 du cercle, C. R. Acad. Sc. Paris, 299 (1984), 145-147. | MR | Zbl

[Co1] C. Conley. Isolated invariant sets and the Morse index, CBMS Regional Conference, 38, Providence RI, Amer. Math. Soc., 1978. | MR | Zbl | DOI

[Co2] C. Conley. The gradient structure of aflow (I), Ergod. Th. Dynam. Sys., 8* (1988), 11-31. | MR | Zbl | DOI

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

[CZ] C. Conley, E. Zehnder. The Birkhoff-Lewis fixed point theorem and a conjecture of Arnold, Invent. Math., 73 (1983), 33-49. | MR | Zbl | EuDML | DOI

[D] J. Denzler. Mather sets for plane Hamiltonian systems. J. Appl. Math. Phys. (ZAMP), 38 (1987), 791-812. | MR | Zbl | DOI

[Do] R. Douady. Application du théorème des tores invariants, Thèse de troisième cycle, Univ. Paris VII, 1982.

[EE] C. Earle, J. Eells. A fibrebundle description of Teichmuller theory, J. Differential Geometry, 4 (1970), 169-185.

[Fa1] A. Fathi. Une interprétation plus topologique de la démonstration du théorème de Birkhoff, Appendice du Chap. I de [Hm2].

[Fa2] A. Fathi. An orbit closing proof of Brouwer's lemma on translation arcs, L'enseignement Math., 33 (1987), 315-322. | MR | Zbl

[Fa3] A. Fathi. Expansiveness, hyperbolicity and Hausdorff dimension. Comm. in Math. Phys., 126 (1989), 249-262. | MR | Zbl | DOI

[FLP] A. Fathi, F. Laudenbach, V. Poenaru. Travaux de Thurston sur les surfaces, Astérisque, 66-67, Soc. Math. France, (1979). | MR | Numdam | Zbl

[F1] 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 | Zbl | DOI

[Fr1] J. Franks. Generalizations of the Poincaré-Birkhoff theorem, Ann. of Math., 128 (1988), 139-151. | MR | Zbl | DOI

[Fr2] J. Franks. Recurrence and fixed points of surface homeomorphisms, Ergod. Th. Dynam. Sys., 8* (1988), 99-107. | MR | Zbl | DOI

[Fr3] J. Franks. A variation on the Poincaré-Birkhoff theorem, Contemporary Mathematics, 81 (1988), 111-117. | MR | Zbl | DOI

[Fr4] J. Franks. Realizing rotation vectors for torus homeomorphisms, Trans. Amer. Math. Soc., 311 (1989), 107-115. | MR | Zbl | DOI

[Gol] C. Gole. Ghost circle for twist maps, preprint, University of Minnesota, (1990). | Zbl | MR

[Gor] D. L. Goroff. Hyperbolic sets for twist maps, Ergod. Th. Dynam. Sys., 5 (1985), 337-354. | MR | Zbl | DOI

[Gu] L. Guillou. Théorème de translation plane de Brouwer et généralisations du théorème de Poincaré-Birkhoff, preprint, Univ. Paris-Sud, (1990). | MR | Zbl

[Ha1] G. R. Hall. A topological version of a theorem of Mather on twist maps. Ergod. Th. Dynam. Sys., 4 (1984), 585-603. | MR | Zbl

[Ha2] G. R. Hall. Some problems on dynamics of annulus maps, Contemporary Mathematics, 81 (1988), 135-151. | MR | Zbl | DOI

[Hd1] M. Handel. A pathological area preserving C diffeomorphism of the plane, Proc. Amer. Math. Soc., 86 (1982), 163-168. | MR | Zbl

[Hd2] M. Handel. Zero entropy surfaces homeomorphisms, preprint, CUNY, (1986).

[Hd3] M. Handel. The rotation set of a homeomorphism is closed, Comm. Math. Phys., 127 (1990), 339-349. | MR | Zbl | DOI

[H1] G. A. Hedlund. Geodesics on a two-dimensional Riemannian manifold with periodic coefficients. Ann. of Math., 33 (1932), 719-739. | MR | JFM | DOI

[Hn] M. Henon. A two-dimensional mapping with a strange attractor, Comm. Math. Phys., 50 (1976), 69-77. | MR | Zbl | DOI

[Hm1] M. R. Herman. Sur la conjugaison différentiate des difféomorphismes du cercle à une rotation. Publ. Math. I.H.E.S., 49 (1979), 5-234. | MR | Zbl | EuDML | Numdam | DOI

[Hm2] M. R. Herman. Sur les courbes invariantes par les difféomorphismes de l'anneau, Astérisque, 103-104, Soc. Math. France, (1983). | MR | Zbl | Numdam

[Hm3] M. R. Herman. Inégalités à priori pour des tores lagrangiens invariants par des difféomorphismes symplectiques, Publ. Math. I.H.E.S., 70 (1989), 47-101. | MR | Zbl | EuDML | Numdam | DOI

[Hm4] M. Herman. On the dynamics on Lagrangian tori invariant by symplectic diffeomorphisms, preprint, Ecole Polytechnique, (1990). | MR | Zbl

[HH] K. Hockett, P. Holmes. Josephson's junction, annulus maps, Birkhoff attractors, horseshoes and rotation sets, Ergod. Th. Dynam. Sys., 6 (1986), 205-239. | MR | Zbl | DOI

[Hu] M. Hurley. Attractors : persistence, and density of their basins, Trans. Amer. Math. Soc., 269 (1982), 247-271. | MR | Zbl | DOI

[Ka1] A. Katok. Lyapounov exponents, entropy and periodic points for diffeomorphisms, Publ. Math. I.H.E.S., 51 (1980). | MR | Zbl | Numdam | DOI

[Ka2] A. Katok. Some remarks on Birkhoff and Mather twist map theorem, Ergod. Th. Dynam. Sys., 2 (1982), 185-194. | MR | Zbl | DOI

[Ka3] A. Katok. Minimal orbits for small perturbations of completely integrable Hamiltonian systems, preprint, Cal. Tech. | Zbl | MR

[Ke] B. De Kerekjarto. The plane translation theorem of Brouwer and the last geometric theorem of Poincaré, Acta Sci. Math. Szeged, 4 (1928-29), 86-102. | JFM

[Ku] I. Kupka. Contribution à la théorie des champs génériques, Contributions to Diff. Equations, 2 (1963), 457-484. | MR | Zbl

[L1] P. Le Calvez. Existence d'orbites quasi-périodiques dans les attracteurs de Birkhoff, Commun. Math. Phys., 106 (1986), 383-394. | MR | Zbl | DOI

[L2] P. Le Calvez. Propriétés dynamiques des régions d'instabilité, Ann. Scient. Ec. Norm. Sup., 20 (1987), 443-464. | MR | Zbl | EuDML | Numdam | DOI

[L3] P. Le Calvez. Propriétés des attracteurs de Birkhoff, Ergod. Th. Dynam. Sys. 8 (1987), 241-310. | MR | Zbl

[L4] P. Le Calvez. Les ensembles d'Aubry-Mather d'un difféomorphisme conservatif de l'anneau déviant la verticale sont en général hyperboliques. C. R. Acad. Sci. Paris. 306 (1988), 51-54. | MR | Zbl

[L5] P. Le Calvez. Propriétés générales des applications déviant la verticale. Bull. Soc. Math. France, 117 (1989), 69-102. | MR | Zbl | EuDML | Numdam | DOI

[L6] P. Le Calvez. Etude topologique des applications déviant la verticale, Ensaios Matematicos, Soc. Bras. Math., vol. 2 (1990). | EuDML | Zbl

[L7] P. Le Calvez. Existence d' orbites de Birkhoff généralisées pour les difféomorphismes conservatifs de l'anneau, preprint, Univ. Paris-Sud, (1989).

[L8] P. Le Calvez. Construction d'orbites périodiques par perturbation d'un difféomorphisme déviant la verticale, preprint, Univ. Paris-Sud, (1991). | MR | Zbl

[Lv] M. Levi. Qualitative analysis of the periodically forced relaxation oscillations, Mem. Amer. Math. Soc., 24 (1981), 1-147. | MR | Zbl

[Ln] N. Levinson. A second order differential equation with singular solutions, Ann. of Math., 50 (1949), 127-153. | MR | Zbl | DOI

[Li1] J. E. Littlewood. On non linear differential equations of the second order : III, Acta Math., 97 (1957), 267-308. | MR | Zbl

[Li2] J. E. Littlewood. On non linear differential equations of the second order : IV, Acta Math., 98 (1957), 1-110. | MR | Zbl

[LM] J. Llibre, R. S. Mackay. Rotation vectors and entropy for diffeomorphisms of the torus isotopic to the identity, Ergod. Th and Dynam. Sys., 11 (1991), 115-128. | MR | DOI

[Ma1] J. Mather. Invariant subsets of area-preserving homeomorphisms of surfaces, Advances in Math. Suppl. Studies, 7B. | Zbl

[Ma2] J. Mather. Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology, 21 (1982), 457-467. | MR | Zbl | DOI

[Ma3] J. Mather. Glancing billards, Ergod. Th. Dynam. Sys. 2 (1982), 397-403. | MR | Zbl | DOI

[Ma4] J. Mather. Non-uniqueness of solutions of Percival's Euler-Lagrange equation, Comm. Math. Phys., 86 (1982), 465-473. | MR | Zbl | DOI

[Ma5] J. Mather. A criterion for the non-existence of invariant circles, Publ. IHES, 63 (1986), 153-204. | MR | Zbl | EuDML | Numdam | DOI

[Ma6] J. Mather. Destruction of invariant circles Ergod. Th. Dynam. Sys., 8* (1988), 199-214. | MR | Zbl | DOI

[Ma7] J. Mather. Minimal measures, Comment. Math. Helv., 64 (1989), 375-394. | MR | Zbl | EuDML | DOI

[Ma8] J. Mather. Minimal action measures for positive definite Lagrangian systems, a paraître dans Proc. IXth Int. Conf. Math. Phys. | Zbl

[Ma9] J. Mather. Variational construction of orbits of twist diffeomorphisms, (1990). | Zbl

[MS] R. S. Mac Kay, J. Stark. Lectures on orbits of minimal actions for area preserving maps, preprint, Univ. of Warwick.

[Mi] J. Milnor, On the concept of attactor, Comm. Math. Phys., Commun. Math. Phys., 99 (1985), 177-195. | MR | Zbl | DOI

[MZ1] M. Misiurewicz, K. Zieman. Rotation sets for maps of tori, preprint, Univ. of Warwick, 1988. | Zbl | MR

[MZ2] M. Misiurewicz, K. Zieman. Rotation sets and ergodic measures for torus homeomorphism, Fund. Math., 137 (1991), 45-52. | MR | Zbl | EuDML | DOI

[MV] L. Mora, M. Viana. Abundance of strange attractors, preprint, IMPA, Rio de Janeiro, (1989). | MR | Zbl

[Mo1] J. Moser. On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss., Gottingen, Math. Phys., KI (1962), 1-20. | MR | Zbl

[Mo2] J. Moser. Monotone twist mappings and the calculus of variation, Ergod. Th. Dynam. Sys., 6 (1986), 401-413. | MR | Zbl | DOI

[Mo3] J. Moser. Recent developments in the theory of Hamiltonian systems, SIAM Review, 8 (1986), 459-485. | MR | Zbl

[N1] S. Newhouse. Diffeomorphisms with infinitely many sinks Topology, 13 (1974), 9-18. | MR | Zbl | DOI

[N2] S. Newhouse. The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms, Publ. Math. I.H.E.S., 50 (1979), 101-151. | MR | Zbl | EuDML | Numdam | DOI

[NPT] S. E. Newhouse, J. Palis, F. Takens. Bifurcations and stability of families of diffeomorphisms, Publ. Math. I.H.E.S., 57 (1983), 5-72. | MR | Zbl | EuDML | Numdam | DOI

[PT] J. Palis, F. Takens. Homoclinic bifurcations : hyperbolicity, fractional dimension and infinitely many attractors, Cambridge Univers. Press, à paraître. | Zbl

[P1] P. Plykin. Sources and sinks for A-diffeomorphisms, USSR Math. Sb. 23 (1978), 233-253. | Zbl | DOI

[Po] H. Poincare. Sur un théorème de géométrie, Rediconti del Circolo Matematico di Palermo, 33 (1912), 375-407. | JFM | DOI

[Ro] R. C. Robinson. Generic properties of conservative systems : I, II, Amer. J. Math., 92 (1970), 562-603 et 897-906. | Zbl | MR | DOI

[Ru] D. Ruelle. Small random perturbations of dynamical systems and the definition of attractors, Commun. Math. Phys., 82 (1981), 137-151. | MR | Zbl | DOI

[Sc] S. Schwartzman. Asymptotic cycles, Ann. of Maths, 68 (1957), 270-284. | MR | Zbl | DOI

[SM] C. L. Siegel, J. K. Moser. Lectures on celestial mechanics, Springer-Verlag, Berlin, (1971). | MR | Zbl

[Sm1] S. Smale, Stable manifolds for differential equations and diffeomorphisms, Ann. Scuola Norm. Sup. Pisa, 17 (1963), 97-116. | MR | EuDML | Numdam | Zbl

[Sm2] S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. | MR | Zbl | DOI

[Sm3] S. Smale, Diffeomorphisms of the 2-sphere, Proc. Amer. Math. Soc., 10 (1959), 621-626. | MR | Zbl

[T] W. P. Thurston. On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc., 19 (1988), 417-431. | MR | Zbl | DOI