Modélisation de la transition vers la turbulence
Séminaire Bourbaki : volume 1982/83, exposés 597-614, Astérisque, no. 105-106 (1983), Talk no. 607, p. 179-197
@incollection{SB_1982-1983__25__179_0,
     author = {Iooss, G\'erard},
     title = {Mod\'elisation de la transition vers la turbulence},
     booktitle = {S\'eminaire Bourbaki : volume 1982/83, expos\'es 597-614},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {105-106},
     year = {1983},
     note = {talk:607},
     pages = {179-197},
     zbl = {0604.76041},
     mrnumber = {728988},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1982-1983__25__179_0}
}
Iooss, Gérard. Modélisation de la transition vers la turbulence, in Séminaire Bourbaki : volume 1982/83, exposés 597-614, Astérisque, no. 105-106 (1983), Talk no. 607, pp. 179-197. http://www.numdam.org/item/SB_1982-1983__25__179_0/

[1] A. Arnéodo, P. Coullet, C. Tresser, Occurence of strange attractors in three-dimensional Volterra equations, Phys.Lett. 79A, 4, 259, (1980) | MR 590579

[2] A. Arnéodo, P. Coullet, C. Tresser, Oscillators with chaotic behavior, J.Stat.Phys., 27,1, 171, (1982) | MR 656874 | Zbl 0522.58033

[3] V. Arnold, Chapitres supplémentaires de la Théorie des Equations Différentielles ordinaires, MIR, Moscou, (1980) | MR 626685 | Zbl 0455.34001

[4] D. G. Aronson, M. A. Chory, G .R. Hall, R. P. Mcgehee, Bifurcations from an invariant circle for two-parameter families of maps of the plane, Comm.Math.Phys. 83, 303, (1982) | MR 649808 | Zbl 0499.70034

[5] P. Bergé, M. Dubois, P. Manneville, Y. Pomeau, Intermittency in Rayleigh-Bénard convection, J. de Phys. Lettres 41, L341, (1980)

[6] M. Brachet, D. Meiron, S. Orszag, B. Nickel, R. Morf, U. Frisch, J.Fluid.Mech., (1982), (à paraître)

[7] A. Chenciner, Bifurcations de difféomorphismes de IR2, au voisinage d'un point fixe elliptique. Chaotic behavior of deterministic systems, Les Houches Summer school 1981, North Holland, (à paraître) | MR 806175 | Zbl 0582.58025

[8] P. Collet, J. P. Eckmann,Iterated maps on the interval as dynamical systems, P. Ph 1, Birkhaüser, Boston, 1980 | MR 613981 | Zbl 0458.58002

[9] M. Dubois, P. Bergé, V. Croquette, Study of non steady convective regimes using Poincaré sections, J.de Phys.Lettres 43, L295, (1982)

[10] J. P. Eckmann, Route to chaos with special emphasis on period doubling. Chaotic behavior of deterministic systems, Les Houches Summer school 1981, North Holland, (à paraître) | Zbl 0616.58032

[11] C. Foias, G. Prodi, Rend. Sem. Math., Univ. Padova 39, 1, (1967) | Numdam | MR 223716 | Zbl 0176.54103

[12] C. Foias, O. P. Manley, R. Témam, I. M. Trèves, Number of modes governing two-dimensional viscous incompressible flows, Phys. Rev. Lett., 50, 14, p. 1031-1034, 1983. | MR 700069

[13] H. Fujita, T. Kato, On the Navier-Stokes initial value problem I, Arch. Rat. Mech. Anal. 16, 4 , 269, (1964) | MR 166499 | Zbl 0126.42301

[14] M. Giglio, S. Musazzi, U. Perini, Transition to chaos via a well ordered sequence of period doubling bifurcations, Phys.Rev.Lett. 47, 243, (1981)

[15] J. P. Gollub, S. V. Benson, Many routes to turbulent convection, J.Fluid Mech.,100, 3, 449, (1980)

[16] J. Guckenheimer, On a codimension two bifurcation, Dynamical Systems and Turbulence, p.99, Lecture Notes in Math., 898, Springer Verlag, 1981 | MR 654886 | Zbl 0482.58006

[17] M. Hénon, Y. Pomeau, Two strange attractors with a simple structure, Turbulence and Navier Stokes equations, Orsay 1975, Lecture Notes in Math 565, (1976) | MR 448436 | Zbl 0379.76049

[18] J. H. Curry, J. R. Herring, J. Loncaric, S. A. Orszag, Order and disorder in two and three dimensional Bénard convection, (preprint).

[19] E. Hopf, A mathematical example displaying features of turbulence, Comm. Pure & Appl. Math. 1, 303, (1948) | MR 30113 | Zbl 0031.32901

[20] G. Iooss, Sur la deuxième bifurcation d'une solution stationnaire de systèmes du type Navier-Stokes, partie II, Arch.Rat.Mech.Anal. 64, 339, (1977) | MR 650472 | Zbl 0356.35068

[21] G. Iooss, Bifurcation of maps and applications, North Holland Math.Studies 36, Amsterdam, 1979 | MR 531030 | Zbl 0408.58019

[21]2G. Iooss, Persistance d'un cercle invariant par une application voisinede "l'application temps T "d'un champ de vecteurs intégrable(I&II), CR.Ac.Sci.Paris A, 1982 (à paraître) | Zbl 0526.34033

[22] A. Chenciner, G. Iooss, Bifurcations de tores invariants, Arch.Rat.Mech.Anal, 69, 2, 109-198 et 71, 301-306, (1979) | MR 521266 | Zbl 0405.58033

[23] V. I. Iudovich, On the stability of steady flows of a viscous incompressible fluid, D.A.N. SSSR, 161, 5, 1037, (1965) | Zbl 0139.21901

[24] L. Landau, E. Lifchitz, Mécanique des fluides, p.131-132, MIR, Moscou 1971

[25] O. E. Lanford Iii, Smooth transformations of intervals, Séminaire Bourbaki,n°563, 1980 | Numdam | Zbl 0514.58028

[26] O. E. Lanford Iii, Introduction to the mathematical theory of dynamical systems, Chaotic behavior of deterministic systems, Les Houches Summer school 1981, North Holland (à paraître) | Zbl 0565.58027

[27] O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon & Breach (2nd ed.), New York 1969 | MR 254401 | Zbl 0184.52603

[28] O. A. Ladyzhenskaya, Mathematical analysis of Navier-Stokes equations for incompressible liquids, Annual Rev. Fluid Mech. 7, 249, (1975) | Zbl 0344.76014

[29] E. N. Lorenz, Deterministic nonperiodic flow, J. Atm. Sci. 20, 130, (1963)

[30] J. Maurer, A. Libchaber, Rayleigh-Bénard experiment in liquid helium; frequency locking and the onset of turbulence, J. de Phys.Lettres 40, L419, (1979)

[31] M. Misiurewicz, Maps of an internal. Chaotic behavior of deterministic systems, Les Houches Summer school 1981, North Holland, (à paraître) | Zbl 0565.58025

[32] S. E. Newhouse, The creation of non-trivial recurrence in the dynamics of diffeomorphisms. Chaotic behavior of deterministic systems, Les Houches Summer school 1981, North Holland (à paraître) | Zbl 0556.58017

[33] Y. Pomeau, P. Manneville, Intermittency and the Lorenz model, Physics Lett. 75A,1, (1979) | MR 594556

[34] D. Ruelle, F. Takens, On the nature of turbulence, Comm. Math. Phys.,20, 167-192, (1971) | MR 284067 | Zbl 0223.76041

[35] L. P. Shil'Nikov, Sov.Math.Dokl.,6, 163, (1965), et Mat.USSR, Sb.10, 91, (1970) | MR 193352

[36] R. Témam, Navier-Stokes equations, North Holland, Amsterdam, 1977 | MR 769654 | Zbl 0383.35057

[37] C. Vidal, A. Pacault (éd.), Nonlinear phenomena in chemical dynamics, Springer Series in Synergetics 12, Springer Verlag, (1981) | MR 689902

[38] R. F. Williams, The structure of Lorenz attractors, Turbulence seminar, Berkeley 1976-77, Lecture Notes in Math. 615, p.94, (1977). | MR 461581 | Zbl 0363.58005