Homoclinic tangencies near cascades of period doubling bifurcations
Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) no. 3, pp. 255-299.
@article{AIHPC_1998__15_3_255_0,
     author = {Catsigeras, Eleonora and Enrich, Heber},
     title = {Homoclinic tangencies near cascades of period doubling bifurcations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {255--299},
     publisher = {Gauthier-Villars},
     volume = {15},
     number = {3},
     year = {1998},
     mrnumber = {1629345},
     zbl = {0912.58025},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1998__15_3_255_0/}
}
TY  - JOUR
AU  - Catsigeras, Eleonora
AU  - Enrich, Heber
TI  - Homoclinic tangencies near cascades of period doubling bifurcations
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1998
SP  - 255
EP  - 299
VL  - 15
IS  - 3
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/item/AIHPC_1998__15_3_255_0/
LA  - en
ID  - AIHPC_1998__15_3_255_0
ER  - 
%0 Journal Article
%A Catsigeras, Eleonora
%A Enrich, Heber
%T Homoclinic tangencies near cascades of period doubling bifurcations
%J Annales de l'I.H.P. Analyse non linéaire
%D 1998
%P 255-299
%V 15
%N 3
%I Gauthier-Villars
%U http://archive.numdam.org/item/AIHPC_1998__15_3_255_0/
%G en
%F AIHPC_1998__15_3_255_0
Catsigeras, Eleonora; Enrich, Heber. Homoclinic tangencies near cascades of period doubling bifurcations. Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) no. 3, pp. 255-299. http://archive.numdam.org/item/AIHPC_1998__15_3_255_0/

[1] M. Benedicks and L. Carleson, The dynamics of the Hénon map, Annals of Math., Vol. 133, 1991, pp. 73-169. | MR | Zbl

[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. | Zbl

[3] P. Coullet and C. Tresser, Iterations d'endomorphisms et groupe de rénormalisation, C.R. Acad. Sci. Paris, 287, 1978, pp. 577-588. | MR | Zbl

[4] A.M. Davie, Period doubling for C2+ε mappings, Preprint Univ. Edinburgh, 1992.

[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. | MR | Zbl

[6] M.J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J. Stat. Physics, Vol. 19, 1978, pp. 25-52 | MR | Zbl

[7] M.J. Feigenbaum, The universal metric properties of non-linear transformations, J. Stat. Physics, Vol. 21, 1979, pp. 669-706 | MR | Zbl

[8] M. Hirsch, C. Pugh and M. Shub, Invariant manifolds, Lect. Notes in Math., Vol. 583, Springer. | MR | Zbl

[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. | MR | Zbl

[10] J.C. Martín-Rivas, Homoclinic bifurcations and cascades of period doubling in higher dimensions, Tese do IMPA., Rio de Janeiro.

[11] L. Mora and M. Viana, Abundance of Strange Attractors, Acta Math., Vol. 171, 1993, pp. 1-71. | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | Numdam | MR | Zbl

[14] J. Palis and W. De Melo, Geometric Theory of Dynamical Systems. An Introduction, Springer-Verlag, 1982, New York. | MR | Zbl

[15] J. Palis and F. Takens, Hyperbolicity and the creation of homoclinic orbits, Annals of Math., Vol. 125, 1987, pp. 337-374. | MR | Zbl

[16] J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations, Cambridge University Press, 1993. | MR | Zbl

[17] J. Palis and M. Viana, High dimension diffeomorphisms displaying infinitely many periodic attractors, Annals Math., Vol. 140, 1994, pp. 207-250. | MR | Zbl

[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.