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Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space
Peter W. Bates and Kening Lu, Brigham Young University, Provo, UT, and Chongchun Zeng, New York University-Courant Institute of Mathematical Sciences, NY
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Memoirs of the American Mathematical Society
1998; 129 pp; softcover
Volume: 135
ISBN-10: 0-8218-0868-0
ISBN-13: 978-0-8218-0868-9
List Price: US$47
Individual Members: US$28.20
Institutional Members: US$37.60
Order Code: MEMO/135/645
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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.

Features:

  • Important theoretical tools for working with infinite-dimensional dynamical systems, such as PDEs.
  • Previously unpublished results.
  • New ideas regarding invariant manifolds.

Readership

Graduate students, research mathematicians, physicists, and engineers working in analysis, applied mathematics, physical sciences and engineering.

Table of Contents

  • Introduction
  • Notation and preliminaries
  • Statements of theorems
  • Local coordinate systems
  • Cone lemmas
  • Center-unstable manifold
  • Center-stable manifold
  • Smoothness of center-stable manifold
  • Smoothness of center-unstable manifold
  • Persistence of invariant manifold
  • Persistence of normal hyperbolicity
  • Invariant manifolds for perturbed semiflow
  • References
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