no. 5
Lorenz attractor through saddle-node bifurcations
Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) no. 5, pp. 589-617 
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     author = {Morales, C. A.},
     title = {Lorenz attractor through saddle-node bifurcations},
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     pages = {589--617},
     year = {1996},
     publisher = {Gauthier-Villars},
     volume = {13},
     number = {5},
     mrnumber = {1409664},
     zbl = {0871.58061},
     language = {en},
     url = {https://www.numdam.org/item/AIHPC_1996__13_5_589_0/}
}
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Morales, C. A. Lorenz attractor through saddle-node bifurcations. Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) no. 5, pp. 589-617. https://www.numdam.org/item/AIHPC_1996__13_5_589_0/

[1] V.S. Afraimovic and L.P. Shilnikov, 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

[2] R. Bamon, R. Labarca, R. Mane and M.J. Pacifico, The explosion of Singular Cycles, Publ. Math. I.H.E.S., Vol. 78, 1993, pp. 207-232. | Zbl | MR | Numdam

[3] L. Diaz, J. Rocha and M. Viana, Saddle Node cycles and prevalence of Strange Attractors, Preprint I.M.P.A. to appear.

[4] J. Guckemheimer and R.F. Williams, Structural Stability of Lorenz Attractor, Pub. Math. I.H.E.S., Vol. 50, 1979, pp. 59-72. | Zbl | MR | Numdam

[5] M. Hirsch and C. Pugh, Stable Manifold and Hyperbolic sets, Global Analysis, Proc. Sym. Pure Math., Vol. 14. | Zbl | MR

[6] M. Hirsch, C.C. Pugh and M. Shub, Invariant Manifold, Lec. Not. in Math., Vol. 583, 1977. | Zbl

[7] M. Kisaka, H. Kokubu and H. Oka, Bifurcations to N-homoclinic orbits and N-periodic orbits in vector field, Journal of Dynamics and Differential Equations, Vol. 5 (2), 1993. | Zbl | MR

[8] E.N. Lorenz, Deterministic non-periodic flow, J. Atmos. Sci., Vol. 20, 1963, pp. 130-141.

[9] L. Mora and M. Viana, Abundance of Strange Attractors, Act. Math., Vol. 171, 1993, pp. 1-71. | Zbl | MR

[10] S. Newhouse, Lectures on dynamical systems, Progress in Math, N. 8, Birkhauser-Boston. Boston. | Zbl | MR

[11] S. Newhouse, D. Ruelle and F. Takens, Occurrence of Strange Axiom A Attractors Near Quasi Periodic Flows on Tm, m ≥ 3, Commun. math. Phys., Vol. 64, 1978, pp. 35-40. | Zbl | MR

[12] R.V. Plykin, Sources and Sinks of A-Diffeomorphisms, Math. Sbornik, Vol. 94 (136) (2), 1974, pp. 233-253. | Zbl | MR

[13] J. Palis and F. Takens, Stability of parametrized families of gradient vector fields, Ann. of Math., Vol. 118, 1983, pp. 383-421. | Zbl | MR

[14] J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, Vol. 35, 1993. | Zbl | MR

[15] A. Rovella, A Dinâmica das perturbações do Atrator de Lorenz Contrativo, These I.M.P.A., serie F-053-Julho/92.

[16] S. Smale, Differentiable dynamical systems, Bull. Am. Math. Soc., Vol. 73, 1967, pp. 747- 817. | Zbl | MR

[17] J. Sotomayor, Ω-Explosion near saddle-node fixed point, Com. Anais Ac. B. Cienc., Vol. 41, No 4, pp. 644 R.1969.

[18] J. Sotomayor, Generic bifurcations of dynamical systems, Dynamical Systems ed. M. M. Peixoto, Acad. Press, 1973, New York. | Zbl | MR

[19] F. Takens, Partially hyperbolic fixed points, Topology, Vol. 10, 1971, pp. 133-147. | Zbl | MR

[20] R.F. Williams, One dimensional non-wandering set, Topology, Vol. 6, 1969, pp. 473-487. | Zbl | MR