zbMATH — the first resource for mathematics

On the nature of turbulence. (English) Zbl 0223.76041

76F05 Isotropic turbulence; homogeneous turbulence
76F20 Dynamical systems approach to turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
Full Text: DOI
[1] Abraham, R., Marsden, J.: Foundations of mechanics. New York: Benjamin 1967.
[2] Bass, J.: Fonctions stationnaires. Fonctions de corrélation. Application à la représentation spatio-temporelle de la turbulence. Ann. Inst. Henri Poincaré. Section B5, 135–193 (1969). · Zbl 0187.51605
[3] Brunovsky, P.: One-parameter families of diffeomorphisms. Symposium on Differential Equations and Dynamical Systems. Warwick 1968–69.
[4] Hirsch, M., Pugh, C. C., Shub, M.: Invariant manifolds. Bull. A.M.S.76, 1015–1019 (1970). · Zbl 0226.58009 · doi:10.1090/S0002-9904-1970-12537-X
[5] —- —- – Invariant manifolds. To appear.
[6] Hopf, E.: Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems. Ber. Math.-Phys. Kl. Sächs. Akad. Wiss. Leipzig94, 1–22 (1942).
[7] Kelley, A.: The stable, center-stable, center, center-unstable, and unstable manifolds. Published as Appendix C of R. Abraham and J. Robbin: Transversal mappings and flows. New York: Benjamin 1967.
[8] Landau, L. D., Lifshitz, E. M.: Fluid mechanics. Oxford: Pergamon 1959. · Zbl 0146.22405
[9] Leray, J.: Sur le mouvement d’un liquide visqueux emplissant l’espace. Acta Math.63, 193–248 (1934). · JFM 60.0726.05 · doi:10.1007/BF02547354
[10] Moser, J.: Perturbation theory of quasiperiodic solutions of differential equations. Published in J. B. Keller and S. Antman: Bifurcation theory and nonlinear eigenvalue problems. New York: Benjamin 1969.
[11] Smale, S.: Differentiable dynamical systems. Bull. Am. Math. Soc.73, 747–817 (1967). · Zbl 0202.55202 · doi:10.1090/S0002-9904-1967-11798-1
[12] Thom, R.: Stabilité structurelle et morphogénèse. New York: Benjamin 1967.
[13] Williams, R. F.: One-dimensional non-wandering sets. Topology6, 473–487 (1967). · Zbl 0159.53702 · doi:10.1016/0040-9383(67)90005-5
[14] Berger, M.: A bifurcation theory for nonlinear elliptic partial differential equations and related systems. In: Bifurcation theory and nonlinear eigenvalue problems. New York: Benjamin 1969. · Zbl 0181.11603
[15] Fife, P. C., Joseph, D. D.: Existence of convective solutions of the generalized Bénard problem which are analytic in their norm. Arch. Mech. Anal.33, 116–138 (1969). · Zbl 0193.56601
[16] Krasnosel’skii, M.: Topological methods in the theory of nonlinear integral equations. New York: Pergamon 1964.
[17] Rabinowitz, P. H.: Existence and nonuniqueness of rectangular solutions of the Bénard problem. Arch. Rat. Mech. Anal.29, 32–57 (1968). · Zbl 0164.28704 · doi:10.1007/BF00256457
[18] Velte, W.: Stabilität und Verzweigung stationärer Lösungen der Navier-Stokesschen Gleichungen beim Taylorproblem. Arch. Rat. Mech. Anal.22, 1–14 (1966). · Zbl 0233.76054 · doi:10.1007/BF00281240
[19] Yudovich, V.: The bifurcation of a rotating flow of fluid. Dokl. Akad. Nauk SSSR169, 306–309 (1966). · Zbl 0166.46201
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.