Singular strange attractors on the boundary of morse-smale systems

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 30, Issue 6, 1997, Pages 693-717

  Morales, C A ^a   Pujals, E R ^b  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b IMPA   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031280735     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-9593(97)89936-3     Document Type: Article

References (25)

1. [ACL] V. AFRAIMOVICH, S. N. CHOW and W. LIU, Lorenz type Attractors from Codimension One Bifurcation (J. of Dy. and Diff. Eq., Vol. 7 (2), 1995, pp. 375-407).
2. [AP] V. AFRAIMOVICH and Ya B. PESIN, The Dimension of Lorenz Type Attractors, Gordon and Breach: Harwood Academic (Sov. Math. Phys. Rev., Vol. 6, 1987).
3. [AS] V. S. AFRAIMOVICH and L. P. SHILNIKOV, On attainable Transition from Morse-Smale systems to systems with many periodic motions (Math. U.S.S.R. Izv., Vol. 8, 1974, pp. 1235-1270).
4. [BLMP] R. BAMÓN, R. LABARCA, R. MAÑE and M. J. PACÍFICO The explosion of Singular Cycles (Publ. Math. IHES, Vol. 78, 1993, pp. 207-232).
5. [CP] M. D. CARNEIRO and J. PALIS, Bifurcations and global stability of families of gradients, Publ. Math. IHES, Vol. 70, 1990, pp. 103-168.
6. [DKO] F. DUMORTIER, H. KOKUBU and H. OKA, A degenerate singularity generating geometric Lorenz attractors (Ergod. Th. and Dynam. Sys. Vol. 15, 1995, pp. 833-856.)
7. [DRV] L. DIAZ, J. ROCHA and M. VIANA, Saddle node cycles and prevalence of strange attractors (Invent. Math. 125, 1996, pp. 37-74.)
8. [GS] P. GLENDINNING and C. SPARROW, Prime and renormalisable kneading invariants and the dynamic of expanding Lorenz map (Physica D 62, 1993, pp. 22-50.)
9. [GW] J. GUCKENHEIMER and R. F. WILLIAMS, Structural Stability of Lorenz Attractor (Publ. Math. IHES, Vol.50, 1979, pp. 59-72.)
10. [HPS] M. HIRSCH, C. C. PUGH and M. SHUB, Invariant Manifolds (Lec. Not. in Math., 583.)
11. [LV] S. LUZATTO and M. VIANA, Lorenz-like attractors (preprint to appear.)
12. [Mi] M. MISIUREWICZ, Rotation intervals for a class of maps of the real line into itself, (Ergod. Th. and Dynam. Sys., Vol. 6, 1986, pp. 117-132).
13. [M] C. A. MORALES, Lorenz Attractor through Saddle-Node bifurcations (Ann. Inst. Henri Poincaré 28An. nonlin.). VoL. 13, 1996, pp. 589-617).
14. [MV] L. MORA and M. VIANA, Abundance of Strange Attractors (Acta Math., Vol. 171, 1993, pp. 1-71).
15. [NPT] S. NEWHOUSE, J. PALIS and F. TAKENS, Bifurcations and Stability of families of Diffeomorphism (Publ. Math. IHES, Vol. 57, 1983, pp. 5-57).
16. e serie 26, 1993, pp. 691-700).
17. [PRV] M. J. PACÍFICO, A. ROVELLA and M. VIANA, Persistense of Global Spiraling Attractor , in preparation
18. [PT1] J. PALIS and F. TAKENS, Hyperbolicity and sensitive chaotic dynamic at homoclinic bifurcation (Cambridge University Press, Vol. 35).
19. [PT2] J. PALIS and F. TAKENS, Stability of parametrized families of gradient vector fields (Ann. of Math., Vol. 118, 1993, pp. 383-421).
20. [P] Ya. B. PESIN, Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties (Ergod. Th. and Dynam. Sys., Vol. 12, 1992, pp. 123-151).
21. [Pu] E. R. PUJALS (Thesis IMPA to appear.)
22. [R] A. ROVELLA, A Dinamica das Perturbacoes do Attractor de Lorenz Contrativo (Thesis IMPA serie F-053-Junho/92).
23. [ST] L. P. SHILNIKOV and D. TURAEV, On blue sky catastrophes (To appear in Math. Sov. Dok.)
24. [T] F. TAKENS., Partially hyperbolic fixed points (Topology Vol. 10, 1971, pp. 133-147. )
25. [W] R. F. WILLIAMS, The structure of Lorenz attractors (Publ. Math. IHES, Vol. 50, 1979, pp. 101-152.)