Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale
Moreira, Carlos Gustavo ; Yoccoz, Jean-Christophe
Annales scientifiques de l'École Normale Supérieure, Tome 43 (2010), p. 1-68 / Harvested from Numdam

Soit F 0 un difféomorphisme d’une surface possédant deux fers à cheval Λ,Λ ' tels que W s Λ et W u Λ ' aient en un point q une tangence quadratique isolée. Nous montrons que, si la somme des dimensions transverses de W s Λ et W u Λ ' est strictement plus grande que 1, les difféomorphismes voisins de F 0 tels que W s Λ et W u Λ ' soient stablement tangents au voisinage de q forment une partie de densité inférieure strictement positive en F 0 .

Let F 0 be a surface diffeomorphism with two horseshoes Λ,Λ ' such that W s Λ and W u Λ ' have a quadratic tangency at a point q. We show that, if the sum of the transverse dimension of W s Λ and W u Λ ' is larger than one, the set of diffeomorphisms close to F 0 such that W s Λ and W u Λ ' have a stable tangency near q has positive density at F 0 .

Publié le : 2010-01-01
DOI : https://doi.org/10.24033/asens.2115
Classification:  37D05,  37D20,  37E30
Mots clés: bifurcation homocline, tangence homocline, fer à cheval, dimension fractale
@article{ASENS_2010_4_43_1_1_0,
     author = {Moreira, Carlos Gustavo and Yoccoz, Jean-Christophe},
     title = {Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {43},
     year = {2010},
     pages = {1-68},
     doi = {10.24033/asens.2115},
     mrnumber = {2583264},
     zbl = {1200.37020},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_2010_4_43_1_1_0}
}
Moreira, Carlos Gustavo; Yoccoz, Jean-Christophe. Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale. Annales scientifiques de l'École Normale Supérieure, Tome 43 (2010) pp. 1-68. doi : 10.24033/asens.2115. http://gdmltest.u-ga.fr/item/ASENS_2010_4_43_1_1_0/

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