Existence and persistence of invariant manifolds for semiflows in Banach space
About this Title
Peter W. Bates, Kening Lu and Chongchun Zeng
Publication: Memoirs of the American Mathematical Society
Publication Year 1998: Volume 135, Number 645
ISBNs: 978-0-8218-0868-9 (print); 978-1-4704-0234-1 (online)
MathSciNet review: 1445489
MSC (1991): Primary 58F30; Secondary 34G20, 35B40, 47H20, 58F15, 58F39
Since the early 1970s, mathematicians have tried to extend the work of N. Fenichel and of M. Hirsch, C. Pugh and M. Shub to give conditions under which invariant manifolds for semiflows persist under perturbation of the semiflow. This work provides natural conditions and establishes the desired theorem. The technique is geometric in nature, and in addition to rigorous proofs, an informal outline of the approach is given with useful illustrations.
Important theoretical tools for working with infinite-dimensional dynamical systems, such as PDEs.
Previously unpublished results.
New ideas regarding invariant manifolds.
Graduate students, research mathematicians, physicists, and engineers working in analysis, applied mathematics, physical sciences and engineering.
Table of Contents
- 1. Introduction
- 2. Notation and preliminaries
- 3. Statements of theorems
- 4. Local coordinate systems
- 5. Cone lemmas
- 6. Center-unstable manifold
- 7. Center-stable manifold
- 8. Smoothness of center-stable manifolds
- 9. Smoothness of center-unstable manifolds
- 10. Persistence of invariant manifold
- 11. Persistence of normal hyperbolicity
- 12. Invariant manifolds for perturbed semiflow