We prove that every endomorphism which satisfies Axiom A and the strong transversality conditions is -inverse limit structurally stable. These conditions were conjectured to be necessary and sufficient. This result is applied to the study of unfolding of some homoclinic tangencies. This also achieves a characterization of -inverse limit structurally stable covering maps.
Nous montrons qu'un endomorphisme a son extension naturelle qui est -structurellement stable s'il vérifie l'axiome A et la condition de transversalité forte. Ces conditions étaient conjecturées nécessaires et suffisantes. Ce résultat est appliqué à l'étude des déploiements des tangences homoclines. Aussi, cela accomplit la description des recouvrements dont l'extension naturelle est -structurellement stable.
@article{AIHPC_2017__34_5_1227_0, author = {Berger, Pierre and Kocsard, Alejandro}, title = {Structural stability of the inverse limit of endomorphisms}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1227--1253}, publisher = {Elsevier}, volume = {34}, number = {5}, year = {2017}, doi = {10.1016/j.anihpc.2016.10.001}, zbl = {1383.37018}, mrnumber = {3742522}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2016.10.001/} }
TY - JOUR AU - Berger, Pierre AU - Kocsard, Alejandro TI - Structural stability of the inverse limit of endomorphisms JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 1227 EP - 1253 VL - 34 IS - 5 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2016.10.001/ DO - 10.1016/j.anihpc.2016.10.001 LA - en ID - AIHPC_2017__34_5_1227_0 ER -
%0 Journal Article %A Berger, Pierre %A Kocsard, Alejandro %T Structural stability of the inverse limit of endomorphisms %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 1227-1253 %V 34 %N 5 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2016.10.001/ %R 10.1016/j.anihpc.2016.10.001 %G en %F AIHPC_2017__34_5_1227_0
Berger, Pierre; Kocsard, Alejandro. Structural stability of the inverse limit of endomorphisms. Annales de l'I.H.P. Analyse non linéaire, Volume 34 (2017) no. 5, pp. 1227-1253. doi : 10.1016/j.anihpc.2016.10.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2016.10.001/
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