Abstract

In the traditional use of mathematical models showing what is vaguely called chaotic behavior, the number of variables is very large. This may refer to turbulence in aerodynamics or to economic models. The very influential discovery of E.N. Lorenz is that this behavior is not necessarily caused by the size of the system. In his case the system was a 3-variable differential equation and similar constructions can also be made in two variable nonautonomous equations. At this point the subject became accessible for mathematical analysis. The purpose of this report is to describe some of the mechanisms and definitions which have emerged with a focus on some aspects in which I have been personally involved. In many applications one is interested in the long time behavior of solutions of

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