Dynamical Systems
Persistence of stratifications of normally expanded laminations

Presented by: Étienne Ghys

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

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.

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.

Received:
Accepted:
Published online:
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, Volume 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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