Scaling Function Dynamics
In September 1979, P. Hohenberg gave me a picture which showed the first preliminary results of A. Libchaber’s experiment on liquid helium , the power spectrum of a measured signal (Fig. 1). It was immediately clear that the picture had something to do with period doubling, but how it was that one was supposed to understand a one-dimensional theory for a discrete dynamics in order to learn what a fluid was doing was in no way very clear. Over a period of a few months, I tried to understand the picture, and, in the end, was lead to an idea that I have called the scaling function . In these lectures, I shall try to explain what the idea is that came out of this observation and while doing so, discuss the idea that goes under the name of “presentation functions” . I will indicate what these notions mean and explain how from that picture you can determine what is actually the most interesting part of the dynamics.
KeywordsSpectral Line Scaling Function Return Time Period Doubling Linear Restriction
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