Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale
[Stable homoclinic tangencies for hyperbolic sets of large fractal dimension]
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 43 (2010) no. 1, pp. 1-68.

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 .

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 .

DOI: 10.24033/asens.2115
Classification: 37D05,  37D20,  37E30
Keywords: homoclinic bifurcation, homoclinic tangency, horseshoe, fractal dimension
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Moreira, Carlos Gustavo; Yoccoz, Jean-Christophe. Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 43 (2010) no. 1, pp. 1-68. doi : 10.24033/asens.2115. http://www.numdam.org/articles/10.24033/asens.2115/

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