On the ergodic approach for the study of chaotic linear infinite dimensional systems

Abstract

In this work, we will be interested in the study of chaotic behavior exhibited by some linear infinite-dimensional systems. Our tool for this is the theory of chaotic linear semigroups of operators, and we will make use of the imaginary eigenvalues of the infinitesimal generator to construct an invariant Gaussian measure with respect to which the associated semigroup will be strong mixing. An application to the dynamic of a size-structured cell population is given.