no. 2
Mathematical analysis
Non-uniformly hyperbolic horseshoes in the standard family
[Fers à cheval hyperboliques non uniformes dans la famille standard]

Présenté par : Pierre-Louis Lions

Matheus, Carlos1 ; Moreira, Carlos Gustavo2 ; Palis, Jacob2
1 Université Paris-13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), 93439 Villetaneuse, France
2 IMPA, Estrada D. Castorina, 110, CEP 22460-320, Rio de Janeiro, RJ, Brazil
Comptes Rendus. Mathématique, Tome 356 (2018) no. 2, pp. 146-149.

Nous montrons que les fers à cheval hyperboliques non uniformes de Palis et Yoccoz apparaissent dans la famille standard des difféomorphismes du tore de dimension 2 préservant l'aire.

We show that the non-uniformly hyperbolic horseshoes of Palis and Yoccoz occur in the standard family of area-preserving diffeomorphisms of the two-torus.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.12.012
Matheus, Carlos 1 ; Moreira, Carlos Gustavo 2 ; Palis, Jacob 2

1 Université Paris-13, Sorbonne Paris Cité, LAGA, CNRS (UMR 7539), 93439 Villetaneuse, France
2 IMPA, Estrada D. Castorina, 110, CEP 22460-320, Rio de Janeiro, RJ, Brazil 
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     title = {Non-uniformly hyperbolic horseshoes in the standard family},
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Matheus, Carlos; Moreira, Carlos Gustavo; Palis, Jacob. Non-uniformly hyperbolic horseshoes in the standard family. Comptes Rendus. Mathématique, Tome 356 (2018) no. 2, pp. 146-149. doi : 10.1016/j.crma.2017.12.012. http://archive.numdam.org/articles/10.1016/j.crma.2017.12.012/

[1] Duarte, P. Plenty of elliptic islands for the standard family of area preserving maps, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 11 (1994), pp. 359-409

[2] Palis, J.; Yoccoz, J.-C. Non-uniformly hyperbolic horseshoes arising from bifurcations of Poincaré heteroclinic cycles, Publ. Math. Inst. Hautes Études Sci., Volume 110 (2009), pp. 1-217

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