[Persistance des variétés invariantes normalement hyperboliques non-compactes dans la géométrie bornée]
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.
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.
Accepté le :
Publié le :
Jaap Eldering 1
@article{CRMATH_2012__350_11-12_617_0, author = {Jaap Eldering}, title = {Persistence of noncompact normally hyperbolic invariant manifolds in bounded geometry}, journal = {Comptes Rendus. Math\'ematique}, pages = {617--620}, publisher = {Elsevier}, volume = {350}, number = {11-12}, year = {2012}, doi = {10.1016/j.crma.2012.06.009}, language = {en}, }
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] Persistence of overflowing manifolds for semiflow, Comm. Pure Appl. Math., Volume 52 (1999) no. 8, pp. 983-1046
[2] 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] Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J., Volume 21 (1971/1972), pp. 193-226
[5] Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin, 1981
[6] Invariant Manifolds, Lecture Notes in Mathematics, vol. 583, Springer-Verlag, Berlin, 1977
[7] 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] 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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