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Bibliography on Bénard convection experiments (small aspect-ratio)
Bergé, P., M. Dubois, P. Manneville, Y. Pomeau, Intermittency in Rayleigh-Bénard convection, J.de Phys. Lettres 41, L341, 1980
Dubois, M., P. Bergé, V. Croquette,Study of non steady convective regimes using Poincaré sections, J.de Phys. Lettres 43, L295, 1982
Giglio, M., S. Musazzi, U. Perini,Transition to chaos via a well ordered sequence of period doubling bifurcations, Phys. Rev. Lett. 47, 243, 1981
Gollub, J.P., S.V. Benson,Many routes to turbulent convection, J.Fluid Mech.,100, 3, 449, 1980
Maurer, J., A. Libchaber, Rayleigh-Bénard experiment in liquid helium; frequency locking and the onset of turbulence, J.de Phys. Lettres 40, L419, 1979
Review papers on this topic (with lot of references inside)
Busse, F.H.,Transition to turbulence in Rayleigh-Bénard convection, in Hydrodynamic Instabilities and the Transition to Turbulence, H.SWINNEY, J.P.GOLLub ed., Topics in Applied Physics 45, 97–137, Springer Verlag 1981
Gollub, J.P.,Recent experiments on the transition to turbulent convection, Nonlinear Dynamics and Turbulence, G.BARENBLATT, G.IOOSS, D.D.JOSEPH ed., Pitman 1983
Perioddoubling theory for maps of the interval
Collet, P., J.P. Eckmann,Iterated maps on the interval as dynamical systems, P. Ph.1, Birkhaüser, Boston,1980
Bibliography on Couette-Taylor problem
Fenstermacher, P.R., H.L. Swinney, J.P. Gollub,Dynamical instabilities and the transition to chaotic Taylor vortex flow, J.Fluid Mech., 94, 103–128, 1979
Gorman, M., L.A. Reith, H.L. Swinney,Modulation patterns, multiple frequencies and other phenomena in circular Couette flow,Nonlinear Dynamics, R.HELLEMAN ed., Ann. N.Y. Acad. Sci. 357, p.10, 1980
Rand, D.,Dynamics and Symmetry: predictions for modulated waves in rotating fluids, Arch. Rat. Mech. Anal. 79,1, 1–38, 1982
Review paper (lot of references)
Di Prima, R.C., H.L. Swinney,Instabilities and Transition in flow between concentric rotating cylinders, in Hydrodynamic Instabilities and the Transito Turbulence, H.SWINNEY, J.P.GOLLUB ed., Topics in Applied Physics 45, 139–180, Springer Verlag 1981.
Bibliography
Agmon, S.,Lectures on elliptic boundary value problems, Van Nostrand, Math. Studies, 2, Princeton 1965
Brézis, D.,Perturbations singulières et problèmes d'évolution avec défaut d'ajustement, C.R.Acad. Sci. Paris, 276, A, 1597–1600, 1973
Cattabriga, L.,Su un problema al contorno relativo al sistema di equazioni di Stokes, Rendiconti del Seminario Matematico, Padova, vol.31, 308–340, 1961
Fujita, H. & T. Kato,On the Navier-Stokes initial value problem I, Arch.Rat. Mech. Anal. 16, 4, 269–315, 1964
Iooss,G.,Bifurcation et stabilité, Pub. Math. Orsay 31, 1973 (chap.VIIbis), C.R. Acad. Sci. Paris, 271, A, 187–190, 1970
Iooss, G.,Théorie non lineaire de la stabilité des écoulements laminaires dans le cas de l'échange des stabilités, Arch. Rat. Mech. Anal 40, 166–208 (1971)
Iooss, G.,Sur la deuxième bifurcation d'une solution stationnaire de systèmes du type Navier-Stokes, Arch. Rat. Mech. Anal. 64, 4, 339–369, 1977
Iooss, G., & R. Lozi,Convection entre deux plaques planes en rotation, et effet dynamo résultant d'une bifurcation secondaire, J. de Mécanique, 16, 5, 675–703, 1977
Kato, T.,Perturbation theory for linear operators, Springer Verlag, Berlin 1966
Ladyzhenskaya, O.A.,The mathematical theory of viscous incompressible flow, New York, Gordon & Breach, 1963
Pazy, A.,On the differentiability and compactness of semi-groups of linear operators, J.Math. Mech. 17, 12, 1131–1141, 1968
Témam, R.,Navier-Stokes equations, North Holland, Amsterdam, 1977.
Bibliography
Iooss, G., Bifurcation et Stabilité, Pub. Math. Orsay 31,(chap.X), 1973
Iooss, G., & D.D. Joseph, Elementary stability and bifurcation theory, Undergraduate Texts in Math., Springer Verlag, New York, 1980
Kato,T., see ref. [5] of chapter II.
Bibliographical remark for the infinite dimensional case
Iudovich, V.I.,Apparition d'auto-oscillations dans un fluide (in Russian), Prikl. Mat. Mek. 35, 638–655, 1971
Iudovich, V.I.,Etude des auto-oscillations d'un milieu continu, intervenant lors de la perte de stabilité d'un mode stationnaire (in Russian), Prikl. Mat. Mek. 36, 450–459, 1972
Sattinger, D.H.,Bifurcation of periodic solutions of the Navier-Stokes equations, Arch. Rat. Mech. Anal. 41, 66–80, 1971
Sattinger,D.H.,Topic in Stability and Bifurcation theory, Lecture Notes in Math, 309, Springer,1973
Iooss, G.,Existence et Stabilité de la solution périodique secondaire intervenant dans les problèmes d'évolution du type Navier-Stokes, Arch. Rat. Mech. Anal. 47, 301–329, 1972
Marsden,J., M.Mc Cracken,The hopf bifurcation and its applications, Applied Math., 19, Springer Verlag, 1976
Crandall, M.G., & P.H. Rabinovitz,The Hopf bifurcation theorem in infinite dimensions, Arch. Rat. Mech. Anal. 67, 53–72, 1978
Bibliography
Di Prima, R.C. & G.J. Habetler, Arch. Rat. Mech. Anal., 34, 218–227, 1969
Di Prima, R.C., H.L. Swinney, (see ref.[10] of chap.I)
Iooss, G., (see [6] at chap.II)
Joseph,D.D.,Stability of fluid motions I and II, Springer Tracts in Natural Philosophy, New York 1976
Kirchgassner, K.&H. Kielhöfer,Stability and bifurcation in fluid dynamics, Rocky Mountains J.of Math. 3,2, 275–318, 1973
Andereck, C.D., R. Dickman, H.L. Swinney,New flows in a circular Couette system with co-rotating cylinders, Phys.Fluids 26,6, 1395–1401, 1983
For the Bénard problem, about the question of breaking of symmetries
Golubitsky,M., J.W.Swift, E.Knobloch,Symmetries and Pattern Selection in Rayleigh-Bénard convection, (preprint)
Buzano,E., & M.Golubitsky, Phil. Trans. Roy. Soc., 1983
Chossat,P.Le problème de Bénard dans une couche sphérique, Thèse d'Etat, Univ. de Nice, 1982
A more general exposition is in
Sattinger,D.,Group theoretic methods in Bifurcation theory, Lecture Notes in Maths. 762, Springer 1979.
Bibliography
Arnold, V.I., Chapitres supplémentaires de la Théorie des Equations Différentielles ordinaires, MIR, Moscou, 1980
Aronson, D.G., M.A. Chory, G.R. Hall, R.P. Mc Gehee,Bifurcations from an invariant circle for two-parameters families of maps of the plane, Comm.Math.Phys. 83, 303, 1982
Herman, M.,Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ.,I.H.E.S., 49, 1979
Iooss,G.,Bifurcation of maps and applications, North Holland Math.Studies 36, 1979
Iooss, G., A. Arnéodo, P. Coullet, C. Tresser,Simple computation of bifurcating invariant circles for mappings, Lect.Notes in Math. 898,192–211, 1980
Iudovich, V.I.,On the stability of self-oscillations of a liquid, Dokl.Acad. Nauk SSSR 195,3, 574–576 (1970), (in Russian)
Marsden,J., M.Mc Cracken,The Hopf bifurcation and its applications, Applied Math 19, Springer Verlag, 1976
Neimark, J.,On some cases of periodic motions depending on parameters, Dokl. Akad. Nauk. SSR 129, 736–739, (1959), (in Russian)
Rand, D.,Dynamics and Symmetry: Predictions for Modulated Waves in rotating fluids, Arch. Rat. Mech. Anal. 79,1, 1–38, (1982)
Renardy, M.,Bifurcation from rotating waves, Arc.Rat.Mech.Anal. 79,1, 49–84, (1982)
Ruelle, D. & F. Takens,On the nature of turbulence, Comm. Math.Phys. 20, 167–192, 1971
Sacker,R.J.,On invariant surfaces and bifurcation of periodic solutions of ordinary differential equations, New York Univ. IMM.NYU, 333, 1964
See ref.[5] of chapter I
See ref.[2] of chapter I.
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Iooss, G. (1984). Bifurcation and transition to turbulence in hydrodynamics. In: Salvadori, L. (eds) Bifurcation Theory and Applications. Lecture Notes in Mathematics, vol 1057. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098596
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