01212nas a2200145   4500008004100000022001400041245008800055210007000143260000800213300001400221490000700235520076100242100001701003856004601020       2017                        eng d  a1573-869800aSmall Time Asymptotics on the Diagonal for Hörmander's Type Hypoelliptic Operators0 aSmall Time Asymptotics on the Diagonal for Hörmanders Type Hypoe  cJan  a111–1430 v233 a<p>We compute the small time asymptotics of the fundamental solution of Hörmander's type hypoelliptic operators with drift, on the diagonal at a point x0. We show that the order of the asymptotics 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 x0, then so is also the original control problem, and in this case we show that the fundamental solution blows up as t−N/2\$\backslashphantom {\backslashdot {i}\backslash!}t^{-\backslashmathcal {N}/2}\$, where N\$\backslashphantom {\backslashdot {i}\backslash!}\backslashmathcal {N}\$is a number determined by the Lie algebra at x0 of the fields, that define the hypoelliptic operator.</p>1 aPaoli, Elisa  uhttps://doi.org/10.1007/s10883-016-9321-z