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Researcher:
Prof. K. Nipp
Date: 19. 12. 2005
Summary:
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.