Mathematics

We show the small time asymptotic of the fundamental solution for hypoelliptic operators, with drift field, that satisfy weak Hormander condition. We prove that the order of the asymptotic depends on the controllability of an associated control problem and of its approximating system. If the control problem of the approximating system is controllable at $x_0$, then so is also the original control problem, and in this case we show that the fundamental solution blows up as $t^{-N/2}$, where $N$ is a number determined by the Lie algebra at $x_0$ of the fields, that define the hypoelliptic operator.

This seminar is part of the AJS series of seminars.