Comptes Rendus
no. 11-12
Differential Geometry/Dynamical Systems
Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry
[Persistance des variétés invariantes normalement hyperboliques non-compactes dans la géométrie bornée]

Présenté par : the Editorial Board

Jaap Eldering1
1 Mathematical Institute, Utrecht University, Budapestlaan 6, 3584 CD Utrecht, The Netherlands
Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 617-620.

Nous démontrons un résultat de persistance pour les variétés invariantes normalement hyperboliques non-compactes dans une variété riemannienne de géométrie bornée. Il est crucial dʼassumer que la variété ambiante est de géométrie bornée pour contrôler lʼuniformité des estimations tout au long de la preuve.

We prove a persistence result for noncompact normally hyperbolic invariant manifolds in Riemannian manifolds of bounded geometry. The bounded geometry of the ambient manifold is a crucial assumption in order to control the uniformity of all estimates throughout the proof.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.06.009
Jaap Eldering 1

1 Mathematical Institute, Utrecht University, Budapestlaan 6, 3584 CD Utrecht, The Netherlands 
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Jaap Eldering. Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry. Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 617-620. doi : 10.1016/j.crma.2012.06.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.06.009/

[1] Peter W. Bates; Kening Lu; Chongchun Zeng Persistence of overflowing manifolds for semiflow, Comm. Pure Appl. Math., Volume 52 (1999) no. 8, pp. 983-1046

[2] Jürgen Eichhorn The Banach manifold structure of the space of metrics on noncompact manifolds, Differential Geom. Appl., Volume 1 (1991) no. 2, pp. 89-108

[3] Jaap Eldering, Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry, PhD thesis, Utrecht University, 2012, . | arXiv

[4] Neil Fenichel Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J., Volume 21 (1971/1972), pp. 193-226

[5] Daniel Henry Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981

[6] M.W. Hirsch; C.C. Pugh; M. Shub Invariant Manifolds, Lecture Notes in Mathematics, vol. 583, Springer-Verlag, Berlin, 1977

[7] Kunimochi Sakamoto Invariant manifolds in singular perturbation problems for ordinary differential equations, Proc. Roy. Soc. Edinburgh Sect. A, Volume 116 (1990) no. 1–2, pp. 45-78

[8] A. Vanderbauwhede; S.A. van Gils Center manifolds and contractions on a scale of Banach spaces, J. Funct. Anal., Volume 72 (1987) no. 2, pp. 209-224

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