Dynamical Systems
Persistence of stratifications of normally expanded laminations
[Persistance des stratifications de laminations normalement dilatées]

Présenté par : Étienne Ghys

Berger, Pierre1
1 Laboratoire de mathématiques, Université Paris-Sud, bâtiment 425, 91405 Orsay cedex, France
Comptes Rendus. Mathématique, Tome 346 (2008) no. 13-14, pp. 767-772.

On introduit ici la notion de stratification de laminations. On décrit aussi une condition suffisante assurant la persistance des stratifications de laminations préservées par un C1-endomorphisme d'une variété. On présente des applications variées de ce résultat.

We introduce here the concept of stratification of laminations. We explain also a sufficient condition which provides the C1-persistence of a stratification of laminations preserved by a C1-endomorphism of a manifold. We present various applications of this result.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.04.018
Berger, Pierre 1

1 Laboratoire de mathématiques, Université Paris-Sud, bâtiment 425, 91405 Orsay cedex, France 
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Berger, Pierre. Persistence of stratifications of normally expanded laminations. Comptes Rendus. Mathématique, Tome 346 (2008) no. 13-14, pp. 767-772. doi : 10.1016/j.crma.2008.04.018. https://www.numdam.org/articles/10.1016/j.crma.2008.04.018/

[1] Candel, A.; Conlon, L. Foliations. I, Graduate Studies in Mathematics, vol. 23, 2000

[2] de Melo, W. Structural stability of diffeomorphisms on two-manifolds, Invent. Math., Volume 21 (1973), pp. 233-246

[3] Hirsch, M.W.; Pugh, C.C.; Shub, M. Invariant Manifolds, Lecture Notes in Mathematics, vol. 583, 1977

[4] J.N. Mather, Stratifications and mappings, in: Dynamical Systems, Proc. Sympos., Univ. Bahia, Salvador, 1971, 1973, pp. 195–232

[5] Robinson, C. Structural stability of C1 diffeomorphisms, J. Differential Equations, Volume 22 (1976), pp. 28-73

[6] Whitney, H. Local properties of analytic varieties, Differential and Combinatorial Topology (1965), pp. 205-244

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