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

Linearization near a locally nonunique invariant manifold


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.
Citation: George Osipenko. Linearization near a locally nonunique invariant manifold. Discrete & Continuous Dynamical Systems - A, 1997, 3 (2) : 189-205. doi: 10.3934/dcds.1997.3.189

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