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Indestructibility of invariant locally non-unique manifolds
The Sacker-Neimark-Mane result on persistent manifolds of autonomous systems is well-known: an invariant manifold is persistent iff it is normally hyperbolic. The persistent manifolds have the property of the local uniqueness. The paper gives conditions for the indestructibility of an invariant manifold without the supposition of its local uniqueness. These conditions are wider than the normally hyperbolicity conditions. Some examples are considered.