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Invariant Manifolds for Random Dynamical Systems with Slow and Fast Variables

  • Björn SchmalfussEmail author
  • Klaus R. Schneider
Article

We consider random dynamical systems with slow and fast variables driven by two independent metric dynamical systems modeling stochastic noise. We establish the existence of a random inertial manifold eliminating the fast variables. If the scaling parameter tends to zero, the inertial manifold tends to another manifold which is called the slow manifold. We achieve our results by means of a fixed point technique based on a random graph transform. To apply this technique we need an asymptotic gap condition.

Keywords

Random dynamical systems fast–slow system slow manifold inertial manifold 

1991 Mathematics Subject Classifications

37H10 37L25 70K70 

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Institute for MathematicsUniversity of PaderbornPaderbornGermany
  2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

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