Abstract.
We study the existence of attractors for dynamical systems under the influence of random parameters. Such a random attractor is a measurable multi-function with compact images fulfilling particular invariance and attracting properties. In particular, this uniquely determined attractor attracts measurable multi-functions. Under certain conditions we estimate the Hausdorff dimension of the attractor. These results will be applied to the Lorenz system under the influence of a random external parameter perturbation.
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Received: March 27, 1996; revised: December and March 1997
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Schmallfuß, B. The random attractor of the stochastic Lorenz system. Z. angew. Math. Phys. 48, 951–975 (1997). https://doi.org/10.1007/s000330050074
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DOI: https://doi.org/10.1007/s000330050074