Abstract
The immediate source of the concept of entropy of a dynamical system, introduced by A. N. Kolmogorov in 1958, was a definite and typical problem in the context of abstract dynamical systems, the problem of isomorphism. In spite of being so natural, it is far from being immediately evident or soluble. Consider, for instance, a classical case of probabilistic games (mathematically: Bernoulli Shifts): it is quite obvious that, in a repeated experiment, tossing a coin is equivalent to tossing a die and considering the outcomes only in terms of whether they are odd or even; should it also be equivalent to tossing a die and conceiving of the outcomes as ranging from 1 to 6? It was by using his new ‘metric invariant’ — the dynamical or K-entropy — that Kolmogorov succeeded in giving a negative answer to this old and only apparently simple problem.
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