Geodesic
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
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We prove that every endomorphism which satisfies Axiom A and the strong transversality conditions is C1-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 C1-inverse limit structurally stable covering maps.

Nous montrons qu'un endomorphisme a son extension naturelle qui est C1-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 C1-structurellement stable.

DOI : 10.1016/j.anihpc.2016.10.001
Keywords: 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},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1227--1253},
     year = {2017},
     publisher = {Elsevier},
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     number = {5},
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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

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