Invariant manifolds for random dynamical systems with slow and fast variables. (English) Zbl 1138.37032

Schmalfuss, Björn; Schneider, Klaus R.

J. Dyn. Differ. Equations 20, No. 1, 133-164 (2008).

The paper discusses existence of inertial manifolds for a family of random differential equations in \(\mathbb R^{d_1}\times\mathbb R^{d_2}\) with a fast and a slow component, scaled by a factor \(0<\varepsilon\ll1\), where it is assumed that the influence of randomness splits accordingly into a fast and a slow part.

Reviewer: Hans Crauel (Frankfurt)

MSC:

37H99	Random dynamical systems
34F05	Ordinary differential equations and systems with randomness
34C25	Periodic solutions to ordinary differential equations
37D10	Invariant manifold theory for dynamical systems
70K70	Systems with slow and fast motions for nonlinear problems in mechanics

Keywords:

random dynamical system; fast-slow system; inertial manifold; slow manifold; gap condition

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