@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}, publisher = {Soci\'et\'e math\'ematique de France}, number = {204}, year = {1991}, mrnumber = {1183304}, zbl = {0784.58033}, language = {fr}, url = {http://archive.numdam.org/item/AST_1991__204__1_0/} }
Le Calvez, Patrice. Propriétés dynamiques des difféomorphismes de l'anneau et du tore. Astérisque, no. 204 (1991), 133 p. http://numdam.org/item/AST_1991__204__1_0/
[AY] Cascades of period-doubling bifurcations: a prerequisite for horseshoes, Bull. Amer. Math. Soc., 9 (1983), 319-322. | MR | Zbl | DOI
, .[An] Monotone recurrence relations, their Birkhoff orbits and topological entropy, Ergod. Th. Dynam. Sys., 10 (1990), 15-41. | MR | Zbl | DOI
.[AG] Lamination by ghost circles, preprint E.T.H. Zurich (1991).
, .[AL] The discrete Frenkel-Kontorova model and its generalizations, Physica 8D(1983), 381-422. | Zbl
, .[Ba1] Mather sets for twist maps and geodesics on tori, Dynamics reported, Vol I, 1988, John Wiley and Sons. | MR | Zbl | DOI
.[Ba2] Minimal geodesics, Ergod. Th. Dynam. Sys., 10 (1989), 263-286. | MR | Zbl
.[BS] Rotation shadowing properties of circle and annulus maps, Ergod. Th. Dynam. Sys., 8 (1988), 509-521. | MR | Zbl | DOI
, .[BG] Rotation and periodicity in plane separating continua, preprint, Montana State University. | MR | Zbl | DOI
, .[BC] The dynamics of the Hénon map, Ann. of Math., 133 (1991), 73-169. | MR | Zbl | DOI
, .[Be] Birkhoff periodic orbits for twist maps with the circle intersection property, Ergod. Th. Dynam. Sys., 5 (1985), 531-537. | MR | Zbl | DOI
.[BK] 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] Proof of Poincaré's last geometric theorem, Trans. Amer. Math. Soc., 14 (1913), 14-22 | MR | JFM
.Proof of Poincaré's last geometric theorem, Collected Math. Papers, vol I, 673-681, Dover, New-York, (1978).
.[Bi2] Surface transformation and their dynamical applications. Acta Math., 43 (1920), 1-119 ; et Collected Math. Papers, vol II, 111-229. | JFM | MR | DOI
.[Bi3] 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] 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] 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] 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] 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] Periodic points and topological entropy of one dimensional maps, L. N. in Math., 819, Springer Verlag, (1980), 18-34. | MR | Zbl
, , , .[Bo1] Braid Types and a topological method of proving positive entropy, preprint.
.[Bo2] Rotations sets and Morse decomposition in twist maps, Ergod. Th. Dynam. Sys., 8 (1988), 33-61. | MR | Zbl | DOI
.[Bo3] Rotation sets and topologically monotone orbits for annulus homeo-morphisms, preprint, Univ. of Minessota.
.[BH] Invariant circles and the order structure of periodic orbits in monotone twist maps, Topology, 26 (1987), 21-35. | MR | Zbl | DOI
, .[Bw] Entropy and the fundamental group, L. N. in Math. 668, Springer Verlag, (1978), 21-29. | MR | Zbl
.[BF] The periodic points of maps of the disk and the interval, Topology, 15 (1976), 337-342. | MR | Zbl | DOI
, .[Bwr] Beweis des ebenen Translationssatzes, Math. Ann., 72 (1912), 37-54. | MR | JFM | EuDML | DOI
.[Br] A new proof of Brouwer's lemma on translation arcs, Houston J. of Math., 10 (1984), 35-41. | MR | Zbl
.[BN] Proof of the Poincaré-Birkhoff fixed point theorem, Mich. Math. J., 24 (1977), 21-31. | MR | Zbl | DOI
, .[By] Aubry-Mather sets and Birkhoff s theorem for geodesic flows on a two-dimensional torus, preprint, Weizmann Inst., (1988). | MR | Zbl
.[Cr] An improvement of the Poincaré-Birkhoff theorem, Trans. Amer. Math. Soc., 269 (1982), 285-299. | MR | Zbl
.[CL] On non-linear differential equations of the second order : I. The equation large, J. London Math. Soc., 20 (1945), 180-189. | Zbl | MR | DOI
, .[Ci1] Periodic orbits for dissipative twist maps, Ergod. Th. Dynam. Sys., 7 (1987), 165-173. | MR | Zbl | DOI
.[Ci2] Rotational chaos in dissipative systems, Physica 29D (1988), 365-386. | MR | Zbl
.[CB] Automorphisms of surfaces after Nielsen and Thurston, London Math. Soc. Students Texts, 9 (1988). | MR | Zbl
, ,[Chp1] Une idée de "géodésiques brisées" pour les systèmes hamiltoniens, C. R. Acad. Sc. Paris, 298 (1984), 293-296. | MR | Zbl
,[Chp2] An elementary proof of the Conley-Zehnder theorem, L. N. in Math., 1125 (1985), 1-8. | MR | Zbl
.[Chr1] Sur quelques propriétés des courbes de M. Birkhoff, Bull. Soc. Math. France, 62 (1934), 193-224. | MR | Zbl | EuDML | Numdam | DOI
.[Chr2] Sur des courbes fermées analogues aux courbes de M. Birkhoff, J. Math. Pures et Appl., 14 (1935), 1-48. | Zbl | JFM | Numdam
.[Che1] Sur un énoncé dissipatif du théorème géométrique de Poincaré-Birkhoff, C. R. Acad. Sc. Paris, 294 (1982), 243-246. | MR | Zbl
.[Che2] 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] Une remarque sur la structure des endomorphismes de degré du cercle, C. R. Acad. Sc. Paris, 299 (1984), 145-147. | MR | Zbl
, , .[Co1] Isolated invariant sets and the Morse index, CBMS Regional Conference, 38, Providence RI, Amer. Math. Soc., 1978. | MR | Zbl | DOI
.[Co2] The gradient structure of aflow (I), Ergod. Th. Dynam. Sys., 8* (1988), 11-31. | MR | Zbl | DOI
.[CE] Isolated invariant sets and isolating blocks, Trans. Amer. Math. Soc., 158 (1971), 35-61. | MR | Zbl | DOI
, .[CZ] The Birkhoff-Lewis fixed point theorem and a conjecture of Arnold, Invent. Math., 73 (1983), 33-49. | MR | Zbl | EuDML | DOI
, .[D] Mather sets for plane Hamiltonian systems. J. Appl. Math. Phys. (ZAMP), 38 (1987), 791-812. | MR | Zbl | DOI
.[Do] Application du théorème des tores invariants, Thèse de troisième cycle, Univ. Paris VII, 1982.
.[EE] A fibrebundle description of Teichmuller theory, J. Differential Geometry, 4 (1970), 169-185.
, .[Fa1] Une interprétation plus topologique de la démonstration du théorème de Birkhoff, Appendice du Chap. I de [Hm2].
.[Fa2] An orbit closing proof of Brouwer's lemma on translation arcs, L'enseignement Math., 33 (1987), 315-322. | MR | Zbl
.[Fa3] Expansiveness, hyperbolicity and Hausdorff dimension. Comm. in Math. Phys., 126 (1989), 249-262. | MR | Zbl | DOI
.[FLP] Travaux de Thurston sur les surfaces, Astérisque, 66-67, Soc. Math. France, (1979). | MR | Numdam | Zbl
, , .[F1] 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] Generalizations of the Poincaré-Birkhoff theorem, Ann. of Math., 128 (1988), 139-151. | MR | Zbl | DOI
.[Fr2] Recurrence and fixed points of surface homeomorphisms, Ergod. Th. Dynam. Sys., 8* (1988), 99-107. | MR | Zbl | DOI
.[Fr3] A variation on the Poincaré-Birkhoff theorem, Contemporary Mathematics, 81 (1988), 111-117. | MR | Zbl | DOI
.[Fr4] Realizing rotation vectors for torus homeomorphisms, Trans. Amer. Math. Soc., 311 (1989), 107-115. | MR | Zbl | DOI
.[Gol] Ghost circle for twist maps, preprint, University of Minnesota, (1990). | Zbl | MR
.[Gor] Hyperbolic sets for twist maps, Ergod. Th. Dynam. Sys., 5 (1985), 337-354. | MR | Zbl | DOI
.[Gu] Théorème de translation plane de Brouwer et généralisations du théorème de Poincaré-Birkhoff, preprint, Univ. Paris-Sud, (1990). | MR | Zbl
.[Ha1] A topological version of a theorem of Mather on twist maps. Ergod. Th. Dynam. Sys., 4 (1984), 585-603. | MR | Zbl
.[Ha2] Some problems on dynamics of annulus maps, Contemporary Mathematics, 81 (1988), 135-151. | MR | Zbl | DOI
.[Hd1] A pathological area preserving diffeomorphism of the plane, Proc. Amer. Math. Soc., 86 (1982), 163-168. | MR | Zbl
.[Hd2] Zero entropy surfaces homeomorphisms, preprint, CUNY, (1986).
.[Hd3] The rotation set of a homeomorphism is closed, Comm. Math. Phys., 127 (1990), 339-349. | MR | Zbl | DOI
.[H1] Geodesics on a two-dimensional Riemannian manifold with periodic coefficients. Ann. of Math., 33 (1932), 719-739. | MR | JFM | DOI
.[Hn] A two-dimensional mapping with a strange attractor, Comm. Math. Phys., 50 (1976), 69-77. | MR | Zbl | DOI
.[Hm1] 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] Sur les courbes invariantes par les difféomorphismes de l'anneau, Astérisque, 103-104, Soc. Math. France, (1983). | MR | Zbl | Numdam
.[Hm3] 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] On the dynamics on Lagrangian tori invariant by symplectic diffeomorphisms, preprint, Ecole Polytechnique, (1990). | MR | Zbl
.[HH] Josephson's junction, annulus maps, Birkhoff attractors, horseshoes and rotation sets, Ergod. Th. Dynam. Sys., 6 (1986), 205-239. | MR | Zbl | DOI
, .[Hu] Attractors : persistence, and density of their basins, Trans. Amer. Math. Soc., 269 (1982), 247-271. | MR | Zbl | DOI
.[Ka1] Lyapounov exponents, entropy and periodic points for diffeomorphisms, Publ. Math. I.H.E.S., 51 (1980). | MR | Zbl | Numdam | DOI
.[Ka2] Some remarks on Birkhoff and Mather twist map theorem, Ergod. Th. Dynam. Sys., 2 (1982), 185-194. | MR | Zbl | DOI
.[Ka3] Minimal orbits for small perturbations of completely integrable Hamiltonian systems, preprint, Cal. Tech. | Zbl | MR
.[Ke] The plane translation theorem of Brouwer and the last geometric theorem of Poincaré, Acta Sci. Math. Szeged, 4 (1928-29), 86-102. | JFM
.[Ku] Contribution à la théorie des champs génériques, Contributions to Diff. Equations, 2 (1963), 457-484. | MR | Zbl
.[L1] Existence d'orbites quasi-périodiques dans les attracteurs de Birkhoff, Commun. Math. Phys., 106 (1986), 383-394. | MR | Zbl | DOI
.[L2] Propriétés dynamiques des régions d'instabilité, Ann. Scient. Ec. Norm. Sup., 20 (1987), 443-464. | MR | Zbl | EuDML | Numdam | DOI
.[L3] Propriétés des attracteurs de Birkhoff, Ergod. Th. Dynam. Sys. 8 (1987), 241-310. | MR | Zbl
.[L4] 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] Propriétés générales des applications déviant la verticale. Bull. Soc. Math. France, 117 (1989), 69-102. | MR | Zbl | EuDML | Numdam | DOI
.[L6] Etude topologique des applications déviant la verticale, Ensaios Matematicos, Soc. Bras. Math., vol. 2 (1990). | EuDML | Zbl
.[L7] Existence d' orbites de Birkhoff généralisées pour les difféomorphismes conservatifs de l'anneau, preprint, Univ. Paris-Sud, (1989).
.[L8] Construction d'orbites périodiques par perturbation d'un difféomorphisme déviant la verticale, preprint, Univ. Paris-Sud, (1991). | MR | Zbl
.[Lv] Qualitative analysis of the periodically forced relaxation oscillations, Mem. Amer. Math. Soc., 24 (1981), 1-147. | MR | Zbl
.[Ln] A second order differential equation with singular solutions, Ann. of Math., 50 (1949), 127-153. | MR | Zbl | DOI
.[Li1] On non linear differential equations of the second order : III, Acta Math., 97 (1957), 267-308. | MR | Zbl
.[Li2] On non linear differential equations of the second order : IV, Acta Math., 98 (1957), 1-110. | MR | Zbl
.[LM] 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] Invariant subsets of area-preserving homeomorphisms of surfaces, Advances in Math. Suppl. Studies, 7B. | Zbl
.[Ma2] Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology, 21 (1982), 457-467. | MR | Zbl | DOI
.[Ma3] Glancing billards, Ergod. Th. Dynam. Sys. 2 (1982), 397-403. | MR | Zbl | DOI
.[Ma4] Non-uniqueness of solutions of Percival's Euler-Lagrange equation, Comm. Math. Phys., 86 (1982), 465-473. | MR | Zbl | DOI
.[Ma5] A criterion for the non-existence of invariant circles, Publ. IHES, 63 (1986), 153-204. | MR | Zbl | EuDML | Numdam | DOI
.[Ma6] Destruction of invariant circles Ergod. Th. Dynam. Sys., 8* (1988), 199-214. | MR | Zbl | DOI
.[Ma7] Minimal measures, Comment. Math. Helv., 64 (1989), 375-394. | MR | Zbl | EuDML | DOI
.[Ma8] Minimal action measures for positive definite Lagrangian systems, a paraître dans Proc. IXth Int. Conf. Math. Phys. | Zbl
.[Ma9] Variational construction of orbits of twist diffeomorphisms, (1990). | Zbl
.[MS] Lectures on orbits of minimal actions for area preserving maps, preprint, Univ. of Warwick.
, .[Mi] On the concept of attactor, Comm. Math. Phys., Commun. Math. Phys., 99 (1985), 177-195. | MR | Zbl | DOI
,[MZ1] Rotation sets for maps of tori, preprint, Univ. of Warwick, 1988. | Zbl | MR
, .[MZ2] Rotation sets and ergodic measures for torus homeomorphism, Fund. Math., 137 (1991), 45-52. | MR | Zbl | EuDML | DOI
, .[MV] Abundance of strange attractors, preprint, IMPA, Rio de Janeiro, (1989). | MR | Zbl
, .[Mo1] On invariant curves of area-preserving mappings of an annulus, Nachr. Akad. Wiss., Gottingen, Math. Phys., KI (1962), 1-20. | MR | Zbl
.[Mo2] Monotone twist mappings and the calculus of variation, Ergod. Th. Dynam. Sys., 6 (1986), 401-413. | MR | Zbl | DOI
.[Mo3] Recent developments in the theory of Hamiltonian systems, SIAM Review, 8 (1986), 459-485. | MR | Zbl
.[N1] Diffeomorphisms with infinitely many sinks Topology, 13 (1974), 9-18. | MR | Zbl | DOI
.[N2] 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] Bifurcations and stability of families of diffeomorphisms, Publ. Math. I.H.E.S., 57 (1983), 5-72. | MR | Zbl | EuDML | Numdam | DOI
, , .[PT] Homoclinic bifurcations : hyperbolicity, fractional dimension and infinitely many attractors, Cambridge Univers. Press, à paraître. | Zbl
, .[P1] Sources and sinks for -diffeomorphisms, USSR Math. Sb. 23 (1978), 233-253. | Zbl | DOI
.[Po] Sur un théorème de géométrie, Rediconti del Circolo Matematico di Palermo, 33 (1912), 375-407. | JFM | DOI
.[Ro] Generic properties of conservative systems : I, II, Amer. J. Math., 92 (1970), 562-603 et 897-906. | Zbl | MR | DOI
.[Ru] Small random perturbations of dynamical systems and the definition of attractors, Commun. Math. Phys., 82 (1981), 137-151. | MR | Zbl | DOI
.[Sc] Asymptotic cycles, Ann. of Maths, 68 (1957), 270-284. | Zbl | MR | DOI
.[SM] Lectures on celestial mechanics, Springer-Verlag, Berlin, (1971). | MR | Zbl
, .[Sm1] Stable manifolds for differential equations and diffeomorphisms, Ann. Scuola Norm. Sup. Pisa, 17 (1963), 97-116. | MR | EuDML | Numdam | Zbl
,[Sm2] Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. | MR | Zbl | DOI
,[Sm3] Diffeomorphisms of the -sphere, Proc. Amer. Math. Soc., 10 (1959), 621-626. | MR | Zbl
,[T] On the geometry and dynamics of diffeomorphisms of surfaces, Bull. Amer. Math. Soc., 19 (1988), 417-431. | MR | Zbl | DOI
.