Random dynamical systems
type: Item
instance of: scholarly article
title: Random dynamical systems
zbMATH Open document ID: 0805.60048
published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
publication date: 1995-02-02T00:00:00Z
review text: This paper was given as a presentation at the Jahrestagung der DMV in Berlin, 1992. It provides an overview of the theory of random dynamical systems (RDS's), and covers in a very short, but precise way the state of the art in the following areas: 1. Metric, topological, and smooth dynamics, 2. RDS: concept, invariant measures, 3. Generation of RDS, 4. The multiplicative ergodic theorem, 5. Invariant manifolds, stability, 6. Normal forms, Grobman-Hartman theorem, 7. Bifurcation theory, 8. Further areas for research. A list of almost 80 references is provided. The author is currently preparing a monograph ``Random dynamical systems'', which will present the entire area with all the mathematical details.
reviewed by: Wolfgang Kliemann
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 34D08
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 93E03
zbMATH DE Number: 617511
zbMATH Keywords: invariant measures
zbMATH Keywords: multiplicative ergodic theorem
zbMATH Keywords: invariant manifolds
zbMATH Keywords: stability
zbMATH Keywords: stochastic bifurcation
author: Ludwig Arnold
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 617511