We consider a dynamical linear differential (or recurrent) system whose initial state is given only by a probability density. The Shannon information entropy, associated with the probability density, is considered as a global uncertainty index giving a measure of the uncertainty about the state of the system. The law of evolution with time of this index is given. This law remains the same with a global uncertainty index equal to a Rényi informational measure. The purpose of this article is to show how there evolves with time the uncertainty about the state of a dynamical system whose initial state is already imperfectly known. This uncertainty is expressed in probabilistic terms and the dynamical system considered is supposed to be linear. In other words the sensitivity of the dynamical system to initial conditions is considered in an informational frame.
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