@article{AIHPC_1996__13_5_589_0, author = {Morales, C. A.}, title = {Lorenz attractor through saddle-node bifurcations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {589--617}, publisher = {Gauthier-Villars}, volume = {13}, number = {5}, year = {1996}, mrnumber = {1409664}, zbl = {0871.58061}, language = {en}, url = {http://www.numdam.org/item/AIHPC_1996__13_5_589_0/} }
Morales, C. A. Lorenz attractor through saddle-node bifurcations. Annales de l'I.H.P. Analyse non linéaire, Volume 13 (1996) no. 5, pp. 589-617. http://www.numdam.org/item/AIHPC_1996__13_5_589_0/
[1] On Attainable Transitions from Morse-Smale systems to systems with many periodic motions, Math. U.S.S.R. Izv., Vol. 8, 1974, N. 6, pp. 1235-1270. | Zbl
and ,[2] The explosion of Singular Cycles, Publ. Math. I.H.E.S., Vol. 78, 1993, pp. 207-232. | Numdam | MR | Zbl
, , and ,[3] Saddle Node cycles and prevalence of Strange Attractors, Preprint I.M.P.A. to appear.
, and ,[4] Structural Stability of Lorenz Attractor, Pub. Math. I.H.E.S., Vol. 50, 1979, pp. 59-72. | Numdam | MR | Zbl
and ,[5] Stable Manifold and Hyperbolic sets, Global Analysis, Proc. Sym. Pure Math., Vol. 14. | MR | Zbl
and ,[6] Invariant Manifold, Lec. Not. in Math., Vol. 583, 1977. | Zbl
, and ,[7] Bifurcations to N-homoclinic orbits and N-periodic orbits in vector field, Journal of Dynamics and Differential Equations, Vol. 5 (2), 1993. | MR | Zbl
, and ,[8] Deterministic non-periodic flow, J. Atmos. Sci., Vol. 20, 1963, pp. 130-141.
,[9] Abundance of Strange Attractors, Act. Math., Vol. 171, 1993, pp. 1-71. | MR | Zbl
and ,[10] Lectures on dynamical systems, Progress in Math, N. 8, Birkhauser-Boston. Boston. | MR | Zbl
,[11] Occurrence of Strange Axiom A Attractors Near Quasi Periodic Flows on Tm, m ≥ 3, Commun. math. Phys., Vol. 64, 1978, pp. 35-40. | MR | Zbl
, and ,[12] Sources and Sinks of A-Diffeomorphisms, Math. Sbornik, Vol. 94 (136) (2), 1974, pp. 233-253. | MR | Zbl
,[13] Stability of parametrized families of gradient vector fields, Ann. of Math., Vol. 118, 1983, pp. 383-421. | MR | Zbl
and ,[14] Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, Vol. 35, 1993. | MR | Zbl
and ,[15] A Dinâmica das perturbações do Atrator de Lorenz Contrativo, These I.M.P.A., serie F-053-Julho/92.
,[16] Differentiable dynamical systems, Bull. Am. Math. Soc., Vol. 73, 1967, pp. 747- 817. | MR | Zbl
,[17] Ω-Explosion near saddle-node fixed point, Com. Anais Ac. B. Cienc., Vol. 41, No 4, pp. 644 R.1969.
,[18] Generic bifurcations of dynamical systems, Dynamical Systems ed. M. M. Peixoto, Acad. Press, 1973, New York. | MR | Zbl
,[19] Partially hyperbolic fixed points, Topology, Vol. 10, 1971, pp. 133-147. | MR | Zbl
,[20] One dimensional non-wandering set, Topology, Vol. 6, 1969, pp. 473-487. | MR | Zbl
,