Saddle-focus singular cycles and prevalence of hyperbolicity

Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

Volumn 15, Issue 5, 1998, Pages 623-649

  Martín, Bernardo San ^a  

^a UNIVERSIDAD CATÓLICA DEL NORTE   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346303116     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0294-1449(98)80003-6     Document Type: Article

References (13)

1. R. BAMON, R. LABARCA, R. MAÑE and M. J. PACIFICO; The explosion of singular cycles, Publications Mathématiques, I.H.E.S., Vol. 78, 1993, pp. 207-232.
2. L. MORA and M. VIANA, Abundance of strange attractors, Acta Math., Vol. 171, 1993, pp. 1-71.
3. S. NEWHOUSE and J. PALIS; Cycles and bifurcation theory, Ast'erisque, Vol. 31, 1976, pp. 293-301.
4. S. NEWHOUSE, The abundance of wild hyperbolic sets and nonsmooth stable set for diffeomorphisms, Publ. Math. I.H.E.S, Vol. 50, 1979, pp. 101-151.
5. S. NEWHOUSE, J. PALIS and F. TAKENS, Bifurcations and stability of families of diffeomorphisms, Publ. Math, IH.E.S., Vol. 57, 1983, pp. 5-71.
6. e serie t. 26, 1993, pp. 691-700.
7. J. PALIS and F. TAKENS, Cycles and measure of bifurcation sets for two-dimensional diffeomorphims. Inventiones Math., Vol. 82, 1985, pp. 397-422.
8. J. PALIS and F. TAKENS, Hyperbolicity and the creation of homoclinic orbits, Annals of Math., Vol. 125, 1987, pp. 337-374.
9. J. PALIS and F. TAKENS, Hyperbolicity & sensitive chaotic dynamics at homoclinic bifurcations, Cambridge studies in advanced mathematics, Vol. 35.
10. A. ROVELLA, The Dynamics of Perturbations of the contracting Lorenz attractor, Bol. Soc. Bras. Math., Vol. 24, No. 2, 1993, pp. 233-259.
11. B. SAN MARTÍN, Contracting singular cycles. To appears.
12. C. TRESSER, About some theorems by L. P. Sil'nikov, Annals Inst. Henri Poincare., Vol. 40 No. 4, 1984, pp. 441-461.
13. E. WIGGINS, Global bifurcations and chaos, Applied. Mathematical Sciences, Vol. 73, Springer Verlag, pp. 301-306.