Difféomorphismes de Smale des surfaces

Bonatti, C.; Langevin, R.

With the contributions of: Jeandenans, Emmanuelle

Astérisque, no. 250 (1998) , 241 p.

Zbl: 0922.58058

@book{AST_1998__250__R3_0,
     author = {Bonatti, C. and Langevin, R.},
     title = {Diff\'eomorphismes de {Smale} des surfaces},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {250},
     year = {1998},
     zbl = {0922.58058},
     language = {fr},
     url = {http://www.numdam.org/item/AST_1998__250__R3_0/}
}

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%0 Book
%A Bonatti, C.
%A Langevin, R.
%T Difféomorphismes de Smale des surfaces
%S Astérisque
%D 1998
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Bonatti, C.; Langevin, R. Difféomorphismes de Smale des surfaces. Astérisque, no. 250 (1998), 241 p. http://numdam.org/item/AST_1998__250__R3_0/

References
Cited by

[AbSm] R. Abraham, S. Smale, Nongenericity of $Ω$ -stability, Global Analysis I Proc. Symp. Pure Math., 1968, AMS 14 (1970), p. 5-8. | Zbl

[ABS] V. S. Afraimovich, V. V. Bykov et L. P. Shil'Nikov, On the appearance and structure of the Lorenz attractor, Dokl. Acad. Sci. USSR 234, (1977), p. 336-339. | Zbl

[AnPo] A. A. Andronov, L. S. Pontriaguine, systèmes grossiers, Dokl. Akad. Nauk. SSSR, 14 (1937) p. 247-250. | JFM | Zbl

[A1] D. V. Anosov, Geodesic flows on closed riemannian manifolds with negative curvature, Proc. of the Steklov Inst, of Math. (translated by the AMS) 90 (1967). | Zbl

[A2] D. V. Anosov, Structurally stable systems, Proc. Steklov Inst. Math. 169 (1985) p. 61-95. | Zbl

[ArGr1] S. Kh Aranson, V. Z. Grines, The topological classification of cascade on closed two-dimensional manifolds, Russian Math. Surv. 45 N1 (1990) p. 1-35. | DOI | Zbl

[ArGr2] S. Kh Aranson, V. Z. Grines, Cascade on surfaces, Encyclopaedia of Mathematical Sciences 66 Dynamical Systems IX, Springer Verlag (1995) p. 141-175. | DOI

[Be] A. Bezen, On the topological properties and the topological conjugacy of two-dimensional Morse-Smale diffeomorphisms, Random Comput. Dynam. 2 N2 (1994) p. 183-203. | Zbl

[BezGr1] A. N. Bezdenezhnykh, V. Z. Grines, Realization of gradient-like diffeomorphisms of two-dimensional manifolds, N.F. Otrokov (éditeur) Differ. Inte-gral'nyi Uravn., Gor'kij Gos. Univ (1985), p. 33-37. | Zbl

[BezGr2] A. N. Bezdenezhnykh, V. Z. Grines, Diffeomorphism whith orientable he-teroclinic sets on two-dimensional manifolds, E.A. Leontovich-Andronov (éditeur) Trud. Mezhvuz. Temat. Sb. Nauchn. Metody Kachestvennoj Teo-rii Differents Uravn. Gor'kij Gos. Univ. (1985) p. 139-152.

[BezGr3] A. N. Bezdenezhnykh, V. Z. Grines, Dynamical properties and topological classification of gradient-like diffeomorphisms on two-dimensional manifolds, partie 1, E.A. Leontovich-Andronov (éditeur) Trud. Mezhvuz. Temat. Sb. Nauchn. Metody Kachestvennoj Teorii Differents Uravn. Gor'kij Gos. Univ. (1985) 22-38 | Zbl

A. N. Bezdenezhnykh, V. Z. Grines, Dynamical properties and topological classification of gradient-like diffeomorphisms on two-dimensional manifolds, partie 2, E.A. Leontovich-Andronov (éditeur) Trud. Mezhvuz. Temat. Sb. Nauchn. Metody Kachestvennoj Teorii Differents Uravn. Gor'kij Gos. Univ. 1987) p. 24-31. | Zbl

[Bi] G. D. Birkhoff, Nouvelles recherches sur les systèmes dynamiques, Memoriae Pont. Acad. Sci. Novi Lyncaei 93 vol.1 (1935) 85-216 et | JFM | Zbl

G. D. Birkhoff, Nouvelles recherches sur les systèmes dynamiques, œuvres complètes vol. 2 Dover (1968).

[BeHa1] M. Bestvina et M. Handel, Train tracks and automorphisms of free groups, Ann. of Math., 135, (1992) p. 1-51. | DOI | Zbl

[BeHa2] M. Bestvina et M. Handel, Train-tracks for surface homeomorphisms, Topology 34 N.1 (1995) p. 109-140. | DOI | Zbl

[BlFr] P. Blanchard, J. Franks, An obstruction to the existence of certain dynamics in surface diffeomorphisms, Ergod. Th. and Dyn. Sys. 1 (1981) p. 255-260. | Zbl

[Bo1] R. Bowen, Markov partitions for Axiom A diffeomorphisms, Amer. J. of Math. 42 (1970), 725-747. | DOI | Zbl

[Bo2] R. Bowen, Topological entropy and Axiom A, Proc. Symp. Pure Math. Vol 14 AMS, Providence, R.I. (1970) p. 23-41. | DOI | Zbl

[Ch] J. Christy, Branched surfaces and attractors. I : dynamic branched sur faces, Trans. of the AMS 336 N2, april 1993, p. 759-784. | Zbl

[FLP] A. Fathi, F. Laudenbach et V. Poénaru, Travaux de Thurston sur les surfaces, Astérisque 66-67 (1979). | Numdam | Zbl

[Fe] J. Fehrenbach, Roots and symetries of pseudo Anosov homéomorphisms, preprint INLN (1997).

[F1] G. Fleitas, Classification of gradient like flows on dimension two and three, Bol. Soc. Mat. Brasil 6 (1975). | DOI | Zbl | MR

[Fr1] J. Franks, Anosov diffeomorphisms, Proc. Symp. Pure Maths 14 (1970) p. 61-93. | DOI | Zbl | MR

[Fr2] J. Franks, Homology and dynamical systems, volume CBMS 49. Amer. Math. Soc, Providence, Rhode Island (1982). | Zbl | MR

[Fri] D. Fried, Subshifts on surfaces, Ergod. Th. and Dyn. Sys. 2 (1982) p. 15-21. | DOI | Zbl | MR

[Go] C. Godbillon, Eléments de topologie algébrique, Hermann (1971). | Zbl | MR

[Gr1] V. Z. Grines, The topological conjugacy of diffeomorphisms of a two-dimensional manifold on one-dimensional orientable basic set I, (En russe) Trudy Moskow. Mat. Obsch 32 (1975) p. 35-60. | Zbl | MR

[Gr2] V. Z. Grines, The topological conjugacy of diffeomorphisms of a two-dimensional manifold on one-dimensional orientable basic set II, (En russe) Trudy Moskow. Mat. Obsch 34 (1977) p. 243-252. | Zbl | MR

[Gr3] V. Z. Grines, Topological classification of Morse-Smale diffeomorphisms with a finite set of heteroclinic trajectories on surfaces, (En russe) Mat. Zametki 54 N3 (1993) p. 3-17, et traduction dans Math. Notes 54(1993), p. 881-889 (1994). | Zbl | MR

[Gr4] V. Z. Grines, Structural stability and the asymptotic behaviour of invariant manifolds of $A$ -diffeomorphisms of surfaces, Journal of Dynamical and Control Systems 3 N1 (1997) p. 91-110. | DOI | Zbl | MR

[Gr5] V. Z. Grines, On topological classification of structuraly stable diffeomorphisms of surfaces with one-dimensional attractors and repellors, Matem. Sborn. 188 N4 (1997) p. 57-94. | Zbl | MR

[Gr6] V. Z. Grines, Representation of one-dimensional attractors and repellors of $A$ -diffeomorphisms of surfaces by hyperbolic homeomorphisms, Matem. Zametki. (1997) à paraître. | Zbl | MR

[GrKa1] V. Z. Grines, Kh. Kh. Kalay, The topological classification of basic sets with no pairs of conjugate points of $A$ -diffeomorphisms of surfaces, Gorkii State University, Gorkii (1988) p. 1-95.

[GrKa2] V. Z. Grines, Kh. Kh. Kalay, On the topological equivalence of diffeomorphisms with non-trivial basic sets on two-dimensional manifolds, Methods of the qualitative theory of differential equations, Gorkii State University, Gorkii (1988) p. 40-48.

[GuMoNe] J. Guckenheimer, J. Moser, Sh. Newhouse, Dynamical Systems, C.I.M.E. lectures Bressanone, Italy, June 1978, Progress in Math. 8, 1980. | Zbl

[GuWi] J. Guckenheimer et R. F. Williams, Structural stability of Lorenz attractors, Publ. Math. de l'I.H.E.S. 50 (1979), 307-320. | Numdam | EuDML | Zbl | MR

[Ha] J. Hadamard, Sur l'itération et les solutions asymptotiques des équations différentielles, Bull. Soc. Math. France, 29 (1901) p. 223-226. | JFM

[Han] M. Handel, Global shadowing of pseudo-Anosov homeomorphism, Erg. Th. and Dyn. Sys. 5 (1985) p. 373-377. | DOI | Zbl | MR

[He] G. Hemion, On the classification of homéomorphisms of $2$ -manifolds and the classification of $3$ -manifolds, Acta Math1-2 (1979) p. 125-155. | Zbl | MR

[HPPS] M. Hirsch, J. Palis, C. Pugh et M. Shub, Neighbourhoods of hyperbolic sets, Inventiones Math. 9, (1970), p. 121-134. | DOI | EuDML | Zbl | MR

[Je] E. Jeandenans, Difféomorphismes hyperboliques des surfaces et combinatoire des partitions de Markov, thèse de doctorat de l'université de Bourgogne, Dijon, 20 sept 1996.

[La] R. Langevin, Quelques nouveaux invariants des difféomorphismes Morse-Smale d'une surface, Annales Inst. Fourier 43 (1993) Fasc.1 p. 265-278. | DOI | Numdam | EuDML | Zbl | MR

[Lo1] J. Los, Pseudo-Anosov maps and invariant train tracks in the disc : a finite algorithm, Proc. London Math Soc. (1993). | Zbl | MR

[Lo2] J. Los, On the conjugacy problem for automorphisms of free groups, Topology 35, 3,(1996) p. 779-806. | DOI | Zbl | MR

[Lor] E. N. Lorenz, Deterministic nonperiodic flow, J. Atmosph. Sci. 20 (1963), p. 130-141. | DOI | Zbl

[Ma] R. Mane, A proof of the $C^{1}$ -stability conjecture, Publ. Math. I.H.E.S. 66 (1988), p. 161-210. | DOI | Numdam | EuDML | Zbl | MR

[Man] A. Manning, There are no new Anosov diffeomorphisms on tori, Amer. J. Math. 96 (1974), p. 422-429 | DOI | Zbl | MR

[Mar] G. A. Margulis, Certain measures associated with $U$ -flows on compact manifolds, Func. Anal. and its Appl. 4, (1970) p. 55-67. | DOI | MR | Zbl

[Mo] J. Moser, On a theorem of Anosov, J. Diff. Equ. 5 (1969) p. 411-440. | DOI | Zbl | MR

[Mo1] J. Moser, Stable and random motions in dynamical systems, Annals of Math. Studies, Princeton Univ. Press, (1973). | Zbl | MR

[Mos] L. Mosher, The classification of Pseudo-Anosovs, London Math. Soc. Lect. Notes 112 (1986) 13-75. | Zbl | MR

[NePa] S. Newhouse et J. Palis, Hyperbolic nonwandering sets on two-dimensional manifolds, Dyn. Systems, Peixoto ed., Salvador (1973) p. 293-301. | Zbl | MR

[Pa] J. Palis, On Morse-Smale dynamical systems, Topology 8 (1969) p. 385-405. | DOI | Zbl | MR

[PM] J. Palis et W. De Melo, Geometric theory of dynamical systems, Springer-Verlag, (1982). | DOI | Zbl | MR

[PaSm] J. Palis et S. Smale, Structural stability theorems, Proc. of Symposia in Pure Mathematics (Global Analysis) 14 (1970) 223-231. | DOI | Zbl | MR

[PaSu] W. Parry et D. Sullivan, A topological invariant of flows on on one dimensional spaces, Topology 14 (1975), p. 297-299. | DOI | Zbl | MR

[PaTa] J. Palis et F. Takens, Homoclinic bifurcations and chaotic dynamics, Cambridge Uni.Press (1993). | Zbl

[PePe] M. C. Peixoto et M. Peixoto, Structural stability in the plane with enlarged boundary conditions, Anais da Acad. Bras de Ciências 31, (1959). | Zbl | MR

[Pe1] M. Peixoto, Structural stability on two dimensional manifolds, Topology 1, 1962. | DOI | Zbl | MR

[Pe2] M. Peixoto, On the classification of flows on $2$ -manifolds, Salvador Symp. in Dynamical Systems, Academic Press (1973). | Zbl | MR

[Per1] O. Perron, Über Stabilität und asymptotisches Verhalten der Integrale von Differentialgleischungssystemen, Math. Zeit. 29 (1928), p. 129-160. | DOI | EuDML | JFM | MR

[Per2] O. Perron, Über Stabilität und asymptotisches Verhalten der Lösungen eines Systems endlicher Differenzengleichungen, J. Reine Angew. Math 161 (1929), 41-64. | EuDML | JFM | MR

[Per3] O. Perron, Die Stabilitätfrage bei Differentialgleichungen, Math. Zeit.32 (1930), p. 703-728. | DOI | EuDML | JFM | MR

[Pl1] R. V. Plykin, On hyperbolic attractors of diffeomorphisms, Usp.Math. Nauk 35, No 4, (1980) p. 94-104 [English Transl. Russ. Math. Survey 35, No 3, p. 109-121]. | MR | Zbl

[Pl2] R. V. Plykin, On hyperbolic attractors of diffeomorphisms (non-orientable case, Usp.Math. Nauk 35, No 4, (1980) p. 186-187 [English Transl. Russ. Math. Survey 35, No 4, p. 186-187]. | Zbl

[Pl3] R. V. Plykin, On the geometry of hyperbolic attractors of smooth cascades, Usp.Math. Nauk 39, No 6, (1984) 75-113 [English Transl. Russ. Math. Survey 39, No 6, p. 85-131]. | Zbl | MR

[Po] H. Poincaré, Les méthodes nouvelles de la mécanique céleste, Les grands classiques Gauthier-Villars, librairie Blanchard. | JFM | MR

[Pu] C. Pugh, The closing lemma, Amer. J. Math 89 (1967), p. 956-1009. | DOI | Zbl | MR

[PuSh1] C. Pugh, M. Shub, Suspending subshifts, in C. Percelli and R. Sacksteder editors, Contributions to Geometry and Analysis. London Math. Soc., Johns Hopkins University Press, 1981. | Zbl | MR

[Ro] J. W. Robbin, A structural stability theorem, Annals of Math. 94 (1971), p. 447-493. | DOI | Zbl | MR

[R] C. Robinson, Structural stability of $C^{1}$ -diffeomorphisms, J. Diff. Equ. 22 (1976), p. 28-73. | DOI | Zbl | MR

[Ru] G. Ruas, Atratores hiperbólicos de codimensão um e classes de isotopiaem superficies, Informes de Matemática, I.M.P.A. Série F-01/82, (1982) (prépublication).

[Sh] M. Shub, Stabilité globale des systèmes dynamiques, Astérisque 56 (1978). | Numdam | Zbl | MR

[Si] Ya. G. Sinai, Markov partitions and $C$ -diffeomorphisms, Funkts. Anal. Prilozh. 2, No 1, (1968) p.64-69 [English Transl. Funct. Anal. Appl. 2, p. 61-82]. | Zbl | MR

[Sm] S. Smale, Differentiable dynamical systems, Bull. A.M.S. 73 (1967), p. 747-817. | DOI | Zbl | MR

[Wi1] R. Williams, The ' $D A$ ' maps of Smale and structural stability, Global Analysis, Proc. Symp in Pure Math. XIV, Amer. Math Soc (1970), p. 329-334. | DOI | Zbl | MR

[Wi2] R. Williams, Classifications of subshifts of finite type, Annals of Math. 98 (1973) p.120-153 et | DOI | Zbl | MR

R. Williams, Classifications of subshifts of finite type, Errata Annals of Math. 99 (1974) p. 380-381. | DOI | Zbl | MR

[Wi3] R. Williams, Classifications of one-dimensional attractors, Proc. Symp Pure Math. 14 (1970) p. 341-363. | DOI | MR | Zbl