Research Project:

Invariant Manifolds for Maps and Flows

Researcher:  Prof.  K. Nipp

Date:  19. 12. 2005


The theory of invariant manifolds goes back to the work of Hadamard and Perron and was further developed by many authors. In the existing literature there is a strong tendency to formulate the results in a rather general setting. We consider manifolds which may be described by one set of coordinates and we formulate conditions for the Lipschitz constants for maps and flows which are easy to verify and lead to sharp results if the coordinates are chosen appropriately.We investigate attractive, repulsive and hyperbolic invariant manifolds which may be described as the graph of some function and we derive additional results on smoothness, approximations and on foliation. We also investigate applications of invariant manifold theory to numerical analysis.

Prof. K. Nipp
Seminar für Angewandte Mathematik
ETH-Zentrum, HG E13.2
CH-8092 Zürich

Tel.: +41-1-632 34 07
FAX: +41-1-632 16 87

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