Stable intersections of Cantor sets and homoclinic bifurcations
Annales de l'Institut Henri Poincaré. C, Analyse non linéaire, Tome 13 (1996) no. 6, pp. 741-781
@article{AIHPC_1996__13_6_741_0,
     author = {Moreira, Carlos Gustavo T. de A.},
     title = {Stable intersections of {Cantor} sets and homoclinic bifurcations},
     journal = {Annales de l'Institut Henri Poincar\'e. C, Analyse non lin\'eaire},
     pages = {741--781},
     year = {1996},
     publisher = {Gauthier-Villars},
     volume = {13},
     number = {6},
     mrnumber = {1420497},
     zbl = {0865.58035},
     language = {en},
     url = {https://www.numdam.org/item/AIHPC_1996__13_6_741_0/}
}
TY  - JOUR
AU  - Moreira, Carlos Gustavo T. de A.
TI  - Stable intersections of Cantor sets and homoclinic bifurcations
JO  - Annales de l'Institut Henri Poincaré. C, Analyse non linéaire
PY  - 1996
SP  - 741
EP  - 781
VL  - 13
IS  - 6
PB  - Gauthier-Villars
UR  - https://www.numdam.org/item/AIHPC_1996__13_6_741_0/
LA  - en
ID  - AIHPC_1996__13_6_741_0
ER  - 
%0 Journal Article
%A Moreira, Carlos Gustavo T. de A.
%T Stable intersections of Cantor sets and homoclinic bifurcations
%J Annales de l'Institut Henri Poincaré. C, Analyse non linéaire
%D 1996
%P 741-781
%V 13
%N 6
%I Gauthier-Villars
%U https://www.numdam.org/item/AIHPC_1996__13_6_741_0/
%G en
%F AIHPC_1996__13_6_741_0
Moreira, Carlos Gustavo T. de A. Stable intersections of Cantor sets and homoclinic bifurcations. Annales de l'Institut Henri Poincaré. C, Analyse non linéaire, Tome 13 (1996) no. 6, pp. 741-781. https://www.numdam.org/item/AIHPC_1996__13_6_741_0/

[BPV] R. Bamón, S. Plaza and J. Vera, On Central Cantor Sets with self-arithmetic difference of positive Lebesgue measure, to appear in J. London Math. Soc. | Zbl

[H] M. Hall, On the sum and product of continued fractions, Annals of Math., Vol. 48, 1947, pp. 966-993. | Zbl | MR

[MO] P. Mendes and F. Oliveira, On the topological structure of the arithmetic sum of two Cantor sets, Nonlinearity, Vol. 7, 1994, pp. 329-343. | Zbl | MR

[N1] S. Newhouse, Non density of Axiom A(a) on S2, Proc. A.M.S. Symp. Pure Math., Vol. 14, 1970, pp. 191-202. | Zbl | MR

[N2] S. Newhouse, Diffeomorphisms with infinitely many sinks, Topology, Vol. 13, 1974, pp. 9-18. | Zbl | MR

[N3] S. Newhouse, The abundance of wild hyperbolic sets and nonsmooth stable sets for diffeomorphisms, Publ. Math. IHES, Vol. 50, 1979, pp. 101-151. | Zbl | MR | Numdam

[P] J. Palis, Homoclinic bifurcations, sensitive chaotic dynamics and strange attractors, Dynamical Syst. and Related Topics, World Scientific, 1991, pp. 466-473. | MR

[PT] J. Palis and F. Takens, Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms, Invent. Math., Vol. 82, 1985, pp. 379-442. | Zbl | MR

[PT1] J. Palis and F. Takens, Hyperbolicity and the creation of homoclinic orbits, Annals of Math., Vol. 125, 1987, pp. 337-374. | Zbl | MR

[PT2] J. Palis and F. Takens, Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations: fractal dimensions and infinitely many attractors, Cambridge Univ. Press, 1992. | Zbl | MR

[PY] J. Palis and J.C. Yoccoz, Homoclinic Tangencies for Hyperbolic sets of large Hausdorff Dimension Bifurcations, Acta Mathematica, Vol. 172, 1994, pp. 91-136. | Zbl | MR

[S] A. Sannami, An example of a regular Cantor set whose difference set is a Cantor set with positive measure, Hokkaido Math. Journal, Vol. XXI (1), 1992, pp. 7-23. | Zbl | MR