Free access
Issue
ESAIM: M2AN
Volume 34, Number 2, March/April 2000
Special issue for R. Teman's 60th birthday
Page(s) 419 - 437
DOI http://dx.doi.org/10.1051/m2an:2000149
Published online 15 April 2002
  1. R. Abraham and J. Marsden, Foundations of Mechanics, Addison-Wesley: Reading, MA (1978).
  2. D.V. Anosov and V. Arnold, Dynamical Systems I, Springer-Verlag, New York, Heidelberg, Berlin (1985).
  3. V. Arnold, Mathematical Methods of Classical Mechanics, Springer-Verlag, New York, Heidelberg, Berlin (1978).
  4. Alain Bensoussan, Jacques-Louis Lions and Papanicolaou George, Asymptotic analysis for periodic structures, Ser. Studies in Mathematics and its Applications. 5; North-Holland Publishing Co., Amsterdam (1978) 700.
  5. D. Chillingworth, Differential topology with a view to applications. Pitman, London, San Francisco, Melbourne. Research Notes in Mathematics, 9 (1976).
  6. A. Chorin, Vorticity and Turbulence, Springer-Verlag (1994).
  7. P. Constantin and C. Foias, The Navier-Stokes Equations, Univ. of Chicago Press, Chicago (1988).
  8. L. Caffarelli and R. Kohn and L. Nirenberg, On the regularity of the solutions of Navier-Stokes Equations. Comm. Pure Appl. Math. 35 (1982) 771-831. [CrossRef] [MathSciNet]
  9. Strebel, Kurt, Quadratic differentials, Springer-Verlag, Berlin (1984) 184.
  10. A. Fathi, F. Laudenbach and V. Poénaru, Travaux de Thurston sur les surfaces. Asterisque 66-67 (1979).
  11. A. Fannjiang and G. Papanicolaou, Convection enhanced diffusion for periodic flows. SIAM J. Appl. Math. 54 (1994) 333-408. [CrossRef] [MathSciNet]
  12. H. Hopf, Abbildungsklassen n-dimensionaler mannigfaltigkeiten. Math. Annalen 96 (1926) 225-250. [CrossRef]
  13. D. Gottlieb, Vector fields and classical theorems of topology. Rendiconti del Seminario Matematico e Fisico, Milano 60 (1990) 193-203.
  14. J. Milnor, Topology from the differentiable viewpoint. University Press of Virginia, based on notes by D.W. Weaver, Charlottseville (1965).
  15. J. Guckenheimer and P.J. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer-Verlag, New York, Heidelberg, Berlin (1983).
  16. J.K. Hale, Ordinary differential equations, Robert E. Krieger Publishing Company, Malabar, Florida (1969).
  17. M.W. Hirsch, Differential topology, Springer-Verlag, New York, Heidelberg, Berlin (1976).
  18. J.L. Lions, Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris (1969).
  19. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press (1995).
  20. J. Leray, Étude de diverses équations intégrales non linéaires et de quelques problèmes que posent l'hydrodynamique. J. Math. Pures et Appl. XII (1933) 1-82.
  21. J.L. Lions, R. Temam and S. Wang, New formulations of the primitive equations of the atmosphere and applications. Nonlinearity 5 (1992) 237-288. [CrossRef] [MathSciNet]
  22. J.L. Lions, R. Temam and S. Wang, On the Equations of Large-Scale Ocean. Nonlinearity 5 (1992) 1007-1053. [CrossRef] [MathSciNet]
  23. J.L. Lions, R. Temam and S. Wang, Models of the coupled atmosphere and ocean (CAO I). Computational Mechanics Advance, 1 (1993) 3-54.
  24. J.L. Lions, R. Temam and S. Wang, Geostrophic Asymptotics of the Primitive Equations of the Atmosphere. Topological Methods in Nonlinear Analysis 4; note "Special issue dedicated to J. Leray" (1994) 253-287.
  25. J.L. Lions, R. Temam and S. Wang, Mathematical study of the coupled models of atmosphere and ocean (CAO III). J. Math. Pures Appl. 73 (1995) 105-163.
  26. J.L. Lions, R. Temam and S. Wang, A Simple Global Model for the General Circulation of the Atmosphere, "Dedicated to Peter D. Lax and Louis Nirenberg on the occasion of their 70th birthdays''. Comm. Pure. Appl. Math. 50 (1997) 707-752. [CrossRef] [MathSciNet]
  27. P.L. Lions, Mathematical Topics in Fluid Mechanics, Oxford science Publications (1996).
  28. A. Majda, Vorticity and the mathematical theory of incompressible fluid flow. Frontiers of the mathematical sciences: 1985 (New York). Comm. Pure Appl. Math. 39 (1986) S187-S220. [CrossRef]
  29. T. Ma and S. Wang, Dynamics of Incompressible Vector Fields. Appl. Math. Lett. 12 (1999) 39-42. [CrossRef] [MathSciNet]
  30. T. Ma and S. Wang, Dynamics of 2-D Incompressible Flows. Proceedings of the International Conferences on Differential Equations and Computation (1999).
  31. T. Ma and S. Wang, The Geometry of the Stream Lines of Steady States of the Navier-Stokes Equations. Contemporary Mathematics, AMS 238 (1999) 193-202.
  32. T. Ma and S. Wang, Block structure and stability of 2-D Incompressible Flows (in preparation, 1999).
  33. T. Ma and S. Wang, Structural classification and stability of divergence-free vector fields. Nonlinearity (revised, 1999).
  34. A. Majda, The interaction of nonlinear analysis and modern applied mathematics. Proc. Internat. Congress Math., Kyoto, 1990, Springer-Verlag, New York, Heidelberg, Berlin (1991) Vol. 1.
  35. N. Markley, The Poincaré-Bendixson theorem for Klein bottle. Trans. AMS 135 (1969).
  36. L. Markus and R. Meyer, Generic Hamiltonian systems are neither integrable nor ergodic. Memoirs of the American Mathematical Society 144 (1974).
  37. J. Moser, Stable and Random Motions in Dynamical Systems. Ann. Math. Stud. No. 77. Princeton (1973).
  38. J. Palis and W. de Melo, Geometric theory of dynamical systems, Springer-Verlag, New York, Heidelberg, Berlin (1982).
  39. J. Palis and S. Smale, Structural stability theorem. Global Analysis. Proc. Symp. in Pure Math. XIV (1970).
  40. M. Peixoto, Structural stability on two dimensional manifolds. Topology 1 (1962) 101-120. [CrossRef] [MathSciNet]
  41. C. Pugh, The closing lemma. Amer. J. Math. 89 (1967) 956-1009. [CrossRef] [MathSciNet]
  42. Shub, Michael, Stabilité globale des systèmes dynamiques. Société Mathématique de France. Note With an English preface and summary. Astérisque 56 (1978) iv+211.
  43. C. Robinson, Generic properties of conservative systems, I, II. Amer. J. Math. 92 (1970) 562-603 and 897-906.
  44. C. Robinson, Structure stability of vector fields. Ann. of Math. 99 (1974) 154-175. [CrossRef] [MathSciNet]
  45. C. Robinson, Structure stability of C1 diffeomorphisms. J. Differential Equations 22 (1976) 28-73. [CrossRef] [MathSciNet]
  46. G. Schwartz, Hodge decomposition-A method for solving boundary value problems. Lecture Notes in Mathematics 1607 Springer-Verlag (1995).
  47. S. Smale, Differential dynamical systems. Bull. AMS 73 (1967) 747-817. [CrossRef] [MathSciNet]
  48. F. Takens, Hamiltonian systems: generic properties of closed orbits and local perturbations. Math. Ann. 188 (1970) 304-312. [CrossRef] [MathSciNet]
  49. G.I. Taylor, Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. Roy. Soc. A 223 (1923) 289-343. [CrossRef]
  50. R. Temam, Navier-Stokes Equations, Theory and Numerical Analysis, 3rd edition, North Holland, Amsterdam (1984).
  51. R. Thom, Structural Stability and Morphogenesis, Benjamin-Addison Wesley (1975).
  52. W. Thurston, On the geometry and dynamics of diffeomorphisms of surfaces. Bull. AMS 19 (1988) 417-431. [CrossRef] [MathSciNet]
  53. V. Trofimov, Introduction to Geometry on Manifolds with Symmetry, MIA Kluwer Academic Publishers (1994).
  54. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, Heidelberg, Berlin (1990).
  55. J.C. Yoccoz, Recent developments in dynamics, in Proc. Internat. Congress Math., Zurich (1994), Birkhauser Verlag, Basel, Boston, Berlin (1994) 246-265 Vol. 1.

Recommended for you