Lorenz attractor through saddle-node bifurcations

C. A. Morales

Annales de l'I.H.P. Analyse non linéaire (1996)

  • Volume: 13, Issue: 5, page 589-617
  • ISSN: 0294-1449

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Morales, C. A.. "Lorenz attractor through saddle-node bifurcations." Annales de l'I.H.P. Analyse non linéaire 13.5 (1996): 589-617. <http://eudml.org/doc/78394>.

@article{Morales1996,
author = {Morales, C. A.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Lorenz attractor; saddle-node bifurcation; homoclinic tangency},
language = {eng},
number = {5},
pages = {589-617},
publisher = {Gauthier-Villars},
title = {Lorenz attractor through saddle-node bifurcations},
url = {http://eudml.org/doc/78394},
volume = {13},
year = {1996},
}

TY - JOUR
AU - Morales, C. A.
TI - Lorenz attractor through saddle-node bifurcations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1996
PB - Gauthier-Villars
VL - 13
IS - 5
SP - 589
EP - 617
LA - eng
KW - Lorenz attractor; saddle-node bifurcation; homoclinic tangency
UR - http://eudml.org/doc/78394
ER -

References

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  1. [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. Zbl0322.58007
  2. [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. Zbl0801.58010MR1259432
  3. [3] L. Diaz, J. Rocha and M. Viana, Saddle Node cycles and prevalence of Strange Attractors, Preprint I.M.P.A. to appear. Zbl0865.58034
  4. [4] J. Guckemheimer and R.F. Williams, Structural Stability of Lorenz Attractor, Pub. Math. I.H.E.S., Vol. 50, 1979, pp. 59-72. Zbl0436.58018MR556582
  5. [5] M. Hirsch and C. Pugh, Stable Manifold and Hyperbolic sets, Global Analysis, Proc. Sym. Pure Math., Vol. 14. Zbl0215.53001MR271991
  6. [6] M. Hirsch, C.C. Pugh and M. Shub, Invariant Manifold, Lec. Not. in Math., Vol. 583, 1977. Zbl0355.58009
  7. [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. Zbl0784.34038MR1223451
  8. [8] E.N. Lorenz, Deterministic non-periodic flow, J. Atmos. Sci., Vol. 20, 1963, pp. 130-141. 
  9. [9] L. Mora and M. Viana, Abundance of Strange Attractors, Act. Math., Vol. 171, 1993, pp. 1-71. Zbl0815.58016MR1237897
  10. [10] S. Newhouse, Lectures on dynamical systems, Progress in Math, N. 8, Birkhauser-Boston. Boston. Zbl0444.58001MR589590
  11. [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. Zbl0396.58029MR516994
  12. [12] R.V. Plykin, Sources and Sinks of A-Diffeomorphisms, Math. Sbornik, Vol. 94 (136) (2), 1974, pp. 233-253. Zbl0324.58013MR356137
  13. [13] J. Palis and F. Takens, Stability of parametrized families of gradient vector fields, Ann. of Math., Vol. 118, 1983, pp. 383-421. Zbl0533.58018MR727698
  14. [14] J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, Vol. 35, 1993. Zbl0790.58014MR1237641
  15. [15] A. Rovella, A Dinâmica das perturbações do Atrator de Lorenz Contrativo, These I.M.P.A., serie F-053-Julho/92. 
  16. [16] S. Smale, Differentiable dynamical systems, Bull. Am. Math. Soc., Vol. 73, 1967, pp. 747- 817. Zbl0202.55202MR228014
  17. [17] J. Sotomayor, Ω-Explosion near saddle-node fixed point, Com. Anais Ac. B. Cienc., Vol. 41, No 4, pp. 644 R.1969. 
  18. [18] J. Sotomayor, Generic bifurcations of dynamical systems, Dynamical Systems ed. M. M. Peixoto, Acad. Press, 1973, New York. Zbl0296.58007MR339280
  19. [19] F. Takens, Partially hyperbolic fixed points, Topology, Vol. 10, 1971, pp. 133-147. Zbl0214.22901MR307279
  20. [20] R.F. Williams, One dimensional non-wandering set, Topology, Vol. 6, 1969, pp. 473-487. Zbl0159.53702MR217808

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