Bibliographie
J. C. Alexander & J. A. Yorke, Global bifurcation of periodic orbits. Amer. J. of Maths, 100, 2, 263–292 (1978)
V. I. Arnold, Small denominators I, Mappings of the circumference onto itself. Isviestia Akad. Nauk Serie Math. 25.1 (1961) p. 21–86. Translation AMS, 2nd series, 46, 213–284 (1965)
V. I. Arnold & A. Avez, Problèmes ergodiques de la mécanique classique. Gauthier Villars, Paris (1967)
A. Chenciner, Cours à l'Ecole Normale Supérieure, Paris 1977–78
A. Chenciner & G. Iooss, Bifurcation d'un tore T 2 en un tore T 3. C.R. Acad. Sci. Paris, 284, A, 1207–1210 (1977)
bis. A. Chenciner & G. Iooss, Persistance et bifurcation de tores invariants (à paraître)
N. Fenichel, Persistence and smoothness of Invariant Manifolds of Flows. Indiana University Math. J. 21, 3, 193–226 (1971)
W. Gottshalk & G. A. Hedlund, Topological dynamics. AMS colloquium, pub. vol. XXXVI, Providence (1955)
M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Publ. I.H.E.S. Paris (à paraître) [Les renvois sont à la thèse de M. Herman et non au texte définitif]
M. Herman, Mesure de Lebesgue et nombre de rotation. Lecture Notes in Maths. Vol. 597, Springer (1977)
M. W. Hirsch, C. C. Pugh & M. Shub, Invariant manifolds. Lecture Notes in Maths, Vol. 583, Springer (1977)
G. Iooss, Sur la deuxième bifurcation d'une solution stationnaire de systèmes du type Navier-Stokes. Arch. Rational Mech. Anal. 64, 4, 339–369 (1977)
G. Iooss, Cours à l'University of Minnesota, Minneapolis (1977–78)
G. Iooss & D. D. Joseph, Bifurcation and stability of nT-periodic solutions branching from T-periodic solutions at points of resonance. Arch. Rational Mech. Anal. 66, 2, 135–172 (1977)
R. Jost & E. Zehnder, A generalization of Hopf bifurcation theorem. Helvetica Physica Acta, 45, 258–276 (1972)
А. Б. Крыгин, Об ω-предельных множествах цилиндрического каскада. Известия акад. иаук СССР, серия мат. 39, 4, 879–898 (1975)
O. E. Lanford III, Bifurcation of periodic solutions into invariant tori. Lecture Notes in Math, Vol. 322, 159–192, Springer (1973)
J. E. Marsden & M. McCracken, The Hopf bifurcation and its applications. Applied Mathematical Sciences 19, Springer (1976)
D. Ruelle & F. Takens, On the nature of turbulence. Comm. Maths. Phys. 20, 167–192 (1971)
R. J. Sacker, On invariant surfaces and bifurcation of periodic solutions of ordinary differential equations. New York Univ. IMM-NYU, 333 (1964)
S. Sternberg, Celestial Mechanics, part II. Benjamin (1969)
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Chenciner, A., Iooss, G. Bifurcations de tores invariants. Arch. Rational Mech. Anal. 69, 109–198 (1979). https://doi.org/10.1007/BF00281175
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DOI: https://doi.org/10.1007/BF00281175