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Informal remarks on the orbit structure of discrete approximations to chaotic maps. (English) Zbl 0922.58042
It is a fact of experience that computer simulations – of a relatively naive sort – are generally fairly reliable indicators of the properties of concrete dynamical systems. The author presents the results of some computer experiments on the orbit structure of the discrete maps on a finite set which arise when an expanding map of the circle is iterated “naively” on the computer. The author also comments on what mathematical questions ought to be answered in order to account for the reliability in practice of orbit following on the computer as an indicator of the ergodic properties of the underlying map.

MSC:
37A99 Ergodic theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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