The spectral properties of the operators inducing linear dynamical systems on Banach spaces determine the asymptotic properties of the systems. In this note an interaction between the spectral mapping properties of operators and stability properties of the corresponding dynamical systems is presented.

We consider the asymptotic consistency of maximum likelihood parameter estimation for dynamical systems observed with noise. Under suitable conditions on the dynamical systems and the observations, we show that maximum likelihood parameter estimation is consistent. Our proof involves ideas from both information theory and dynamical systems. Furthermore, we show how some well-studied properties ...