, Volume 18, Issue 4, pp 551-571
Date: 02 Oct 2012

Explicit solutions of the \( {\mathfrak{a}_1} \) -type lie-Scheffers system and a general Riccati equation

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Abstract

For a general differential system \( \dot{x}(t) = \sum\nolimits_{d = 1}^3 {u_d } (t){X_d} \) , 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.