Existence and Persistence of Invariant Manifolds for Semiflows in Banach Space

American Mathematical Society (Autor)

Buch | Softcover

1998
American Mathematical Society (Verlag)
978-0-8218-0868-9 (ISBN)

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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.

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. This book features: important theoretical tools for working with infinite-dimensional dynamical systems, such as PDEs; previously unpublished results; and new ideas regarding invariant manifolds.

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.

Erscheint lt. Verlag	30.8.1998
Reihe/Serie	Memoirs of the American Mathematical Society
Zusatzinfo	illustrations
Verlagsort	Providence
Sprache	englisch
Gewicht	260 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	0-8218-0868-0 / 0821808680
ISBN-13	978-0-8218-0868-9 / 9780821808689
Zustand	Neuware