Evolution of uncertainty about the state of a dynamical system

We consider a dynamical linear differential (or recurrent) system whose ini tial 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 t he 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 Renyi informati onal 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 s tate is already imperfectly known. This uncertainty is expressed in probabi listic terms and the dynamical system considered is supposed to be linear. In other words the sensitivity of the dynamical system to initial condition s is considered in an informational frame.