%0 Journal Article
%T Explicit solutions of the $\mathfrak{a}_1$-type Lie-Scheffers system and a general Riccati equation
%A Gabriel Pietrzkowski
%J Mathematics
%D 2014
%I arXiv
%R 10.1007/s10883-012-9159-y
%X For a general differential system $\dot x(t) = \sum_{d=1}^3 u_d(t)X_d$, where $X_d$ generates the simple Lie algebra of type $\mathfrak{a}_1$, we compute the explicit solution in terms of iterated integrals of products of $u_d$'s. As a byproduct we obtain the solution of a general Riccati equation by infinite quadratures.
%U http://arxiv.org/abs/1403.4181v1