Persistence of stratifications of normally expanded laminations

Pierre Berger

doi:10.1016/j.crma.2008.04.018

Dynamical Systems

Persistence of stratifications of normally expanded laminations

Presented by: Étienne Ghys

Pierre Berger ¹

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.

Abstract
Résumé

We introduce here the concept of stratification of laminations. We explain also a sufficient condition which provides the $C^{1}$ -persistence of a stratification of laminations preserved by a $C^{1}$ -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 $C^{1}$ -endomorphisme d'une variété. On présente des applications variées de ce résultat.

Received: 2007-07-27
Accepted: 2008-04-21
Published online: 2008-05-29

DOI: 10.1016/j.crma.2008.04.018

Author's affiliations:

Pierre Berger ¹

¹ Laboratoire de mathématiques, Université Paris-Sud, bâtiment 425, 91405 Orsay cedex, France

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     author = {Pierre Berger},
     title = {Persistence of stratifications of normally expanded laminations},
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     pages = {767--772},
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     language = {en},
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Pierre Berger. 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://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.04.018/

References
Cited by

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

[3] M.W. Hirsch; C.C. Pugh; M. Shub 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] C. Robinson Structural stability of $C^{1}$ diffeomorphisms, J. Differential Equations, Volume 22 (1976), pp. 28-73

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

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