Lorenz attractor through saddle-node bifurcations
Morales, C. A.
Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996), p. 589-617 / Harvested from Numdam
@article{AIHPC_1996__13_5_589_0,
     author = {Morales, Carlos Arnoldo},
     title = {Lorenz attractor through saddle-node bifurcations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {13},
     year = {1996},
     pages = {589-617},
     mrnumber = {1409664},
     zbl = {0871.58061},
     language = {en},
     url = {http://dml.mathdoc.fr/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, Tome 13 (1996) pp. 589-617. http://gdmltest.u-ga.fr/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 0322.58007

[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. | Numdam | MR 1259432 | Zbl 0801.58010

[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. | Numdam | MR 556582 | Zbl 0436.58018

[5] M. Hirsch and C. Pugh, Stable Manifold and Hyperbolic sets, Global Analysis, Proc. Sym. Pure Math., Vol. 14. | MR 271991 | Zbl 0215.53001

[6] M. Hirsch, C.C. Pugh and M. Shub, Invariant Manifold, Lec. Not. in Math., Vol. 583, 1977. | Zbl 0355.58009

[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. | MR 1223451 | Zbl 0784.34038

[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. | MR 1237897 | Zbl 0815.58016

[10] S. Newhouse, Lectures on dynamical systems, Progress in Math, N. 8, Birkhauser-Boston. Boston. | MR 589590 | Zbl 0444.58001

[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. | MR 516994 | Zbl 0396.58029

[12] R.V. Plykin, Sources and Sinks of A-Diffeomorphisms, Math. Sbornik, Vol. 94 (136) (2), 1974, pp. 233-253. | MR 356137 | Zbl 0324.58013

[13] J. Palis and F. Takens, Stability of parametrized families of gradient vector fields, Ann. of Math., Vol. 118, 1983, pp. 383-421. | MR 727698 | Zbl 0533.58018

[14] J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, Vol. 35, 1993. | MR 1237641 | Zbl 0790.58014

[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. | MR 228014 | Zbl 0202.55202

[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. | MR 339280 | Zbl 0296.58007

[19] F. Takens, Partially hyperbolic fixed points, Topology, Vol. 10, 1971, pp. 133-147. | MR 307279 | Zbl 0214.22901

[20] R.F. Williams, One dimensional non-wandering set, Topology, Vol. 6, 1969, pp. 473-487. | MR 217808 | Zbl 0159.53702