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.
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@article{CRMATH_2018__356_2_146_0, author = {Matheus, Carlos and Moreira, Carlos Gustavo and Palis, Jacob}, title = {Non-uniformly hyperbolic horseshoes in the standard family}, journal = {Comptes Rendus. Math\'ematique}, pages = {146--149}, publisher = {Elsevier}, volume = {356}, number = {2}, year = {2018}, doi = {10.1016/j.crma.2017.12.012}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2017.12.012/} }
TY - JOUR AU - Matheus, Carlos AU - Moreira, Carlos Gustavo AU - Palis, Jacob TI - Non-uniformly hyperbolic horseshoes in the standard family JO - Comptes Rendus. Mathématique PY - 2018 SP - 146 EP - 149 VL - 356 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.12.012/ DO - 10.1016/j.crma.2017.12.012 LA - en ID - CRMATH_2018__356_2_146_0 ER -
%0 Journal Article %A Matheus, Carlos %A Moreira, Carlos Gustavo %A Palis, Jacob %T Non-uniformly hyperbolic horseshoes in the standard family %J Comptes Rendus. Mathématique %D 2018 %P 146-149 %V 356 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.12.012/ %R 10.1016/j.crma.2017.12.012 %G en %F CRMATH_2018__356_2_146_0
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://www.numdam.org/articles/10.1016/j.crma.2017.12.012/
[1] 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] 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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