Invariant foliations for random dynamical systems

Ji Li; Kening Lu; Peter W. Bates

doi:10.3934/dcds.2014.34.3639

Article Contents

2014, Volume 34, Issue 9: 3639-3666. Doi: 10.3934/dcds.2014.34.3639

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Invariant foliations for random dynamical systems

1.
Institute for Mathematics and its Application, University of Minnesota, Minneapolis, MN, 55455
2.
Department of Mathematics, Brigham Young University, Provo, Utah 84602
3.
Department of Mathematics, Michigan State University, East Lansing, MI 48824

Received: May 31, 2013

Revised: November 30, 2013

Published: August 2014

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Abstract

We prove the existence of invariant foliations of stable and unstable manifolds of a normally hyperbolic random invariant manifold. The normally hyperbolic random invariant manifold referred to here is that which was shown to exist in a previous paper when a deterministic dynamical system having a normally hyperbolic invariant manifold is subjected to a small random perturbation.

Keywords:

Random dynamical systems,
random normally hyperbolic invariant manifolds,
random invariant foliations.

Mathematics Subject Classification: Primary: 34C37, 34C45, 34F05, 37H10.

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