WIAS Preprint No. 1157, (2006)

Invariant manifolds for random dynamical systems with slow and fast variables



Authors

  • Schmalfuss, Björn
  • Schneider, Klaus R.

2010 Mathematics Subject Classification

  • 37H10 37L25 70K70

Keywords

  • Random dynamical systems, fast-slow system, slow manifold, inertial manifold

Abstract

We consider random dynamical systems with slow and fast variables driven by two independent metric dynamical systems modelling 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.

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