On the Discretization of Double-Bracket Flows

This paper extends the method of Magnus series to Lie-algebraic equations originating in double-bracket ows. We show that the solution of the isospec-tral ow Y 0 = Y; N]; Y ], Y (0) = Y0 2 Sym(n), can be represented in the form Y (t) = e (t) Y0e ?(t) , where the Taylor expansion of can be constructed explicitly , term-by-term, identifying individual expansion terms with certain rooted trees with bicolour leaves. This approach is extended to other Lie-algebraic equations that can be appropriately expressed in terms of a nitèalphabet'.