On the Gap between Random Dynamical Systems and Continuous Skew Products

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Title: On the Gap between Random Dynamical Systems and Continuous Skew Products
Author: Berger, Arno ; Siegmund, Stefan
Abstract: We review the recent notion of a nonautonomous dynamical system (NDS), which has been introduced as an abstraction of both random dynamical systems and continuous skew product flows. Our focus is on fundamental analogies and discrepancies brought about by these two classes of NDS. We discuss base dynamics mainly through almost periodicity and almost automorphy, and we emphasize the importance of these concepts for NDS which are generated by differential and difference equations. Nonautonomous dynamics is presented by means of representative examples. We also mention several natural yet unresolved questions.
Description: AMS 2000 subject classification: primary 37-02, 37B20, 37H05; secondary 34C27, 37A20.
Type: Pre-print
URI: http://hdl.handle.net/1853/29479
Date: 2002
Contributor: Georgia Institute of Technology. School of Mathematics
Relation: CDSNS2002-384
Publisher: Georgia Institute of Technology
Subject: Nonautonomous dynamical systems
Random dynamical systems
Almost periodic equations
Skew product flows
Almost automorphic equations

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