Invariant Foliations near Normally Hyperbolic Invariant Manifolds for Semiflows
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چکیده
Let M be a compact C1 manifold which is invariant and normally hyperbolic with respect to a C1 semiflow in a Banach space. Then in an -neighborhood of M there exist local C1 center-stable and center-unstable manifolds W cs( ) and W cu( ), respectively. Here we show that W cs( ) and W cu( ) may each be decomposed into the disjoint union of C1 submanifolds (leaves) in such a way that the semiflow takes leaves into leaves of the same collection. Furthermore, each leaf intersects M in a single point which determines the asymptotic behavior of all points of that leaf in either forward or backward time.
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تاریخ انتشار 2000