On the Stability and Null-Controllability of an Infinite System of Linear Differential Equations.

In this work, the null controllability problem for a linear system in is considered, where the matrix of a linear operator describing the system is an infinite matrix with on the main diagonal and 1s above it. We show that the system is asymptotically stable if and only if ≤- 1, which shows the fine difference between the finite and the infinite-dimensional systems. When ≤- 1 we also show that the system is null controllable in large.

Variance Continuity for Lorenz Flows.

The classical Lorenz flow, and any flow which is close to it in the -topology, satisfies a Central Limit Theorem (CLT). We prove that the variance in the CLT varies continuously.