Persistance des sous-variétés à bord et à coins normalement dilatées  [ Persistence of normally expanded submanifolds with boundary or corners ]
Annales de l'Institut Fourier, Volume 61 (2011) no. 1, p. 79-104
We show that invariant submanifolds with boundary, and more generally with corners which are normally expanded by an endomorphism are persistent as a-regular stratifications. This result will be shown in class C s , for s1. We present also a simple example of a submanifold with boundary which is normally expanded but non-persistent as a differentiable submanifold.
On se propose de montrer que les variétés à bord et plus généralement à coins, normalement dilatées par un endomorphisme sont persistantes en tant que stratifications a-régulières. Ce résultat sera démontré en classe C s , pour s1. On donne aussi un exemple simple d’une sous-variété à bord normalement dilatée mais qui n’est pas persistante en tant que sous-variété différentiable.
DOI : https://doi.org/10.5802/aif.2598
Classification:  37D10,  57R55
Keywords: Invariant manifold, manifold with boundary, manifold with corner, persistence, normale hyperbolicity, stratification
@article{AIF_2011__61_1_79_0,
     author = {Berger, Pierre},
     title = {Persistance des sous-vari\'et\'es \`a bord et \`a coins normalement dilat\'ees},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {61},
     number = {1},
     year = {2011},
     pages = {79-104},
     doi = {10.5802/aif.2598},
     zbl = {1230.37037},
     mrnumber = {2828127},
     language = {fr},
     url = {https://aif.centre-mersenne.org/item/AIF_2011__61_1_79_0}
}
Berger, Pierre. Persistance des sous-variétés à bord et à coins normalement dilatées. Annales de l'Institut Fourier, Volume 61 (2011) no. 1, pp. 79-104. doi : 10.5802/aif.2598. https://aif.centre-mersenne.org/item/AIF_2011__61_1_79_0/

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