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Nonautonomous and Random Attractors

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Abstract

The theories of nonautonomous and random dynamical systems have undergone extensive, often parallel, developments in the past two decades. In particular, new concepts of nonautonomous and random attractors have been introduced. These consist of families of sets that are mapped onto each other as time evolves and have two forms: a forward attractor based on information about the system in the future and a pullback attractor that uses information about the past of the system. Both reduce to the usual attractor consisting of a single set in the autonomous case.

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Notes

  1. Perhaps Urzeitattraktor would be an appropriate name for a pullback attractor in German.

  2. The term metric or metrical is often used in the literature for historical reasons.

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Authors and Affiliations

  1. Institut für Mathematik, Goethe-Universität, Frankfurt am Main, Germany

    Hans Crauel & Peter E. Kloeden

  2. School of Mathematics and Statistics, Huazhong University of Science & Technology, Wuhan, China

    Peter E. Kloeden

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  1. Hans Crauel
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  2. Peter E. Kloeden
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Correspondence to Hans Crauel.

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Crauel, H., Kloeden, P.E. Nonautonomous and Random Attractors. Jahresber. Dtsch. Math. Ver. 117, 173–206 (2015). https://doi.org/10.1365/s13291-015-0115-0

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