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Properties of center manifolds
1985
Transactions of the American Mathematical Society
The center manifold has a number of puzzling properties associated with the basic questions of existence, uniqueness, differentiability and analyticity which may cloud its profitable application in e.g. bifurcation theory. This paper aims to deal with some of these subtle properties. Regarding existence and uniqueness, it is shown that the cut-off function appearing in the usual existence proof is responsible for the selection of a single center manifold, thereby hiding the inherent
doi:10.1090/s0002-9947-1985-0783998-8
fatcat:cjeo7rl7fbeatprt6iyruxtqxi