Invariant foliations near normally hyperbolic invariant manifolds for semiflows |
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Authors: | Peter W Bates Kening Lu Chongchun Zeng |
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Institution: | Department of Mathematics, Brigham Young University, Provo, Utah 84602 ; Department of Mathematics, Brigham Young University, Provo, Utah 84602 ; Courant Institute of Mathematical Sciences, New York University, New York, New York 10012 |
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Abstract: | Let be a compact manifold which is invariant and normally hyperbolic with respect to a semiflow in a Banach space. Then in an -neighborhood of there exist local center-stable and center-unstable manifolds and , respectively. Here we show that and may each be decomposed into the disjoint union of submanifolds (leaves) in such a way that the semiflow takes leaves into leaves of the same collection. Furthermore, each leaf intersects 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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Keywords: | |
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