Linearization near a locally nonunique invariant manifold

George Osipenko

doi:10.3934/dcds.1997.3.189

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1997, Volume 3, Issue 2: 189-205. Doi: 10.3934/dcds.1997.3.189

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Linearization near a locally nonunique invariant manifold

George Osipenko^1,

1.
Department of Mathematics, State Technical University, St.Petersburg, 194044

Received: August 31, 1996

Published: March 1997

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Abstract

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, 39A12.

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