Abstract
Zeeman has proposed a new notion of structural stability for flows and diffeomorphisms, based on the invariant density functions for associated operators, which correspond to the probability distributions that one would observe in the presence of noise. He gave some examples of stable flows, but only linear examples of stable diffeomorphisms. This paper provides a class of stable non-linear diffeomorphisms of the circle, generalises his ideas to non-invertible maps, and shows the results of numerical computation of the invariant densities for some maps of the interval.
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