Condition of pseudohyperbolic structure
Commun. Korean Math. Soc. 1997 Vol. 12, No. 1, 193-201
Jongheon Kim, George Osipenko
Kumoh National University of Technology, State Technical University
Abstract : The paper presents results on the perturbation problem of invariant manifolds of differential equations. It is well-known that if there is a pseudohyperbolic structure on an invariant manifold then one is strongly indestructible. The set of strongly indestructible invariant manifolds is wider than the set of persistent (normally hyperbolic) manifolds. The following theorem is main result of the paper: if the condition of transversality holds on an invariant manifold, except, possibly, for the non-degenerate strong sources and non-degenerate strong sinks, then there is the pseudohyperbolic structure on the invariant manifold. From this it follows the conditions for the indestructibility of locally non-unique invariant manifolds. An example is considered.
Keywords : pseudohyperbolic structure, transversality, strong source, strong sink
MSC numbers : 34C30, 58F30, 39A12
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