Differentiable invariant manifolds for partially hyperbolic tori and a lambda lemma

Authors
Fontich, E Martin, P
Citation
E. Fontich et P. Martin, Differentiable invariant manifolds for partially hyperbolic tori and a lambda lemma, NONLINEARIT, 13(5), 2000, pp. 1561-1593
Citations number
26
Categorie Soggetti
Mathematics
Journal title
NONLINEARITY
ISSN journal
09517715 → ACNP
Volume
13
Issue
5
Year of publication
2000
Pages
1561 - 1593
Database
ISI
SICI code
0951-7715(200009)13:5<1561:DIMFPH>2.0.ZU;2-D
Abstract
We consider differentiable maps having an invariant torus with normal behav iour and a central part. We prove the existence and regularity of strong-st able manifolds and regularity with respect to the parameters. Then we prove a lambda lemma in this setting for C-2 maps. These results have applicatio ns in the study of diffusion problems, including Arnol'd diffusion. AMS cla ssification scheme numbers: 58F30, 34C35, 34C37.