Structural stability of the inverse limit of endomorphisms

Berger, Pierre; Kocsard, Alejandro

doi:10.1016/j.anihpc.2016.10.001

Berger, Pierre ; Kocsard, Alejandro

Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1227-1253.

Résumé
Abstract

Nous montrons qu'un endomorphisme a son extension naturelle qui est $C^{1}$ -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 $C^{1}$ -structurellement stable.

We prove that every endomorphism which satisfies Axiom A and the strong transversality conditions is $C^{1}$ -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 $C^{1}$ -inverse limit structurally stable covering maps.

MR Zbl

DOI : 10.1016/j.anihpc.2016.10.001

Mots clés : Inverse limit, Natural extension, Structural stability, Axiom A, Endomorphism, Strong transversality condition

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     title = {Structural stability of the inverse limit of endomorphisms},
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Berger, Pierre; Kocsard, Alejandro. Structural stability of the inverse limit of endomorphisms. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 5, pp. 1227-1253. doi : 10.1016/j.anihpc.2016.10.001. http://www.numdam.org/articles/10.1016/j.anihpc.2016.10.001/

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