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April  1997, 3(2): 189-205. doi: 10.3934/dcds.1997.3.189

Linearization near a locally nonunique invariant manifold

George Osipenko 1,

1. 

Department of Mathematics, State Technical University, St.Petersburg, 194044, Russian Federation

Received  September 1996 Published  January 1997

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.
Keywords: Hyperbolic manifold, invariant manifold..
Mathematics Subject Classification: 34C30, 58F30, 39A1.
Citation: George Osipenko. Linearization near a locally nonunique invariant manifold. Discrete & Continuous Dynamical Systems, 1997, 3 (2) : 189-205. doi: 10.3934/dcds.1997.3.189
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