Homoclinic tangencies near cascades of period doubling bifurcations

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1. [1] M. Benedicks and L. Carleson, The dynamics of the Hénon map, Annals of Math., Vol. 133, 1991, pp. 73-169. Zbl0724.58042MR1087346
2. [2] P. Collet, J.P. Eckmann and H. Koch, Period doubling bifurcations for families of maps on Rn, J. Stat. Phys., Vol. 25, N.1, 1981, pp. 1-14. Zbl0521.58041
3. [3] P. Coullet and C. Tresser, Iterations d'endomorphisms et groupe de rénormalisation, C.R. Acad. Sci. Paris, 287, 1978, pp. 577-588. Zbl0402.54046MR512110
4. [4] A.M. Davie, Period doubling for C2+ε mappings, Preprint Univ.Edinburgh, 1992. 
5. [5] J.P. Eckmann and P. Wittwer, 1987, A complete proof of the Feigenbaum conjectures, J. Stat. Physics, Vol. 46, N.3/4, 1987, pp. 455-475. Zbl0683.46052MR883539
6. [6] M.J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Stat. Physics, Vol. 19, 1978, pp. 25-52 Zbl0509.58037MR501179
7. [7] M.J. Feigenbaum, The universal metric properties of non-linear transformations, J. Stat. Physics, Vol. 21, 1979, pp. 669-706 Zbl0515.58028MR555919
8. [8] M. Hirsch, C. Pugh and M. Shub, Invariant manifolds, Lect. Notes in Math., Vol. 583, Springer. Zbl0355.58009MR501173
9. [9] O. Lanford III, A computer assisted proof of the Feigenbaum's conjectures, Bulletin of the A.M.S., Vol. 6, 1982, pp. 427-434. Zbl0487.58017MR648529
10. [10] J.C. Martín-Rivas, Homoclinic bifurcations and cascades of period doubling in higher dimensions, Tese do IMPA., Rio de Janeiro. 
11. [11] L. Mora and M. Viana, Abundance of Strange Attractors, Acta Math., Vol. 171, 1993, pp. 1-71. Zbl0815.58016MR1237897
12. [12] S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math.I.H.E.S. Vol. 50, 1979, pp. 101-151. Zbl0445.58022MR556584
13. [13] S. Newhouse, J. Palis and F. Takens, Bifurcations and Stability of Families of Diffeomorphisms, Publ. Math. I.H.E.S, Vol. 57, 1983, pp. 5-71. Zbl0518.58031MR699057
14. [14] J. Palis and W. De Melo, Geometric Theory of Dynamical Systems. An Introduction, Springer-Verlag, 1982, New York. Zbl0491.58001MR669541
15. [15] J. Palis and F. Takens, Hyperbolicity and the creation of homoclinic orbits, Annals of Math., Vol. 125, 1987, pp. 337-374. Zbl0641.58029MR881272
16. [16] J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, 1993. Zbl0790.58014MR1237641
17. [17] J. Palis and M. Viana, High dimension diffeomorphisms displaying infinitely many periodic attractors, Annals Math., Vol. 140, 1994, pp. 207-250. Zbl0817.58004MR1289496
18. [18] N. Romero, Persistence of homoclinic tangencies in higher dimensions, Tese do IMPA, Rio de Janeiro, 1992. [19] F. Takens, Homoclinic Bifurcations, Proc. Int. Congress of Math., Berkeley, 1986, pp. 1229-1236. [20] M. Viana, Strange attractors in higher dimensions, Tese do IMPA, Rio de Janeiro, 1991. [21] J.A. Yorke and K.T. Alligood, Cascades of period doubling bifurcations: a prerrequisite for horseshoes, Bull. A.M.S., Vol. 9, 1983, pp. 319-322.