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Linearization near a locally nonunique invariant manifold

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  • Theorem of C. Pugh and M. Shub states that a flow can be linearized near normally hyperbolic compact invariant manifold. A normally hyperbolic manifold has the property of local uniqueness. This paper gives conditions for linearization of a flow near an invariant manifold without the assumption of its local uniqueness. These conditions are wider than the normally hyperbolicity condition.
    Mathematics Subject Classification: 34C30, 58F30, 39A12.


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