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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Normally hyperbolic invariant manifolds for random dynamical systems: Part I - persistence


Authors: Ji Li, Kening Lu and Peter Bates
Journal: Trans. Amer. Math. Soc. 365 (2013), 5933-5966
MSC (2010): Primary 34C37, 34C45, 34F05, 37H10
Published electronically: July 10, 2013
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Abstract: In this paper, we prove the persistence of smooth normally hyperbolic invariant manifolds for dynamical systems under random perturbations.


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Additional Information

Ji Li
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
Address at time of publication: Institute for Mathematics and its Application, University of Minnesota, Minneapolis, Minnesota 55455
Email: liji@math.byu.edu, liji@ima.umn.edu

Kening Lu
Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602 – and – School of Mathematics, Sichuan University, Chengdu, People’s Republic of China
Email: klu@math.byu.edu

Peter Bates
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: bates@math.msu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05825-4
PII: S 0002-9947(2013)05825-4
Keywords: Random dynamical systems, random normally hyperbolic invariant manifolds, overflowing manifolds, inflowing manifolds, and random stable and unstable foliations
Received by editor(s): August 30, 2011
Received by editor(s) in revised form: February 28, 2012
Published electronically: July 10, 2013
Additional Notes: The second author was partially supported by NSF0908348
The third author was partially supported by NSF0909400
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.