Invariant foliations near normally hyperbolic invariant manifolds for semiflows

Authors:
Peter W. Bates, Kening Lu and Chongchun Zeng

Journal:
Trans. Amer. Math. Soc. **352** (2000), 4641-4676

MSC (2000):
Primary 37D30, 37L45; Secondary 53C12, 37D10, 37K55

DOI:
https://doi.org/10.1090/S0002-9947-00-02503-4

Published electronically:
June 14, 2000

MathSciNet review:
1675237

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Peter W. Bates**

Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602

Email:
peter@math.byu.edu

**Kening Lu**

Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602

Email:
klu@math.byu.edu

**Chongchun Zeng**

Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012

Email:
zengch@math1.cims.nyu.edu

DOI:
https://doi.org/10.1090/S0002-9947-00-02503-4

Received by editor(s):
December 18, 1996

Received by editor(s) in revised form:
June 5, 1998

Published electronically:
June 14, 2000

Additional Notes:
The first author was partially supported by NSF grant DMS-9622785 and the Isaac Newton Institute

The second author was partially supported by NSF grant DMS-9622853

The third author was partially supported by the Isaac Newton Institute

Article copyright:
© Copyright 2000
American Mathematical Society