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arXiv · 1403.4181

Explicit solutions of the $\mathfrak{a}_1$-type Lie-Scheffers system and a general Riccati equation

Gabriel Pietrzkowski
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Abstract

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.

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Gabriel Pietrzkowski. 2014-03-17. Explicit solutions of the $\mathfrak{a}_1$-type Lie-Scheffers system and a general Riccati equation. https://doi.org/10.1007/s10883-012-9159-y

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