# Two turning points in invariant theory

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We prove the existence of an invariant measure for a large class of random processes with discrete time without assuming their linearity. Our main examples are â€œprocesses with variable lengthâ€, in which components may appear and disappear in the course of functioning. One of these...

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Measuring the average information that is necessary to describe the behavior of a dynamical system leads to a generalization of the Kolmogorovâ€“Sinai entropy. This is particularly interesting when the system has null entropy and the information increases less than linearly with respect to...