Abstract

This paper extends the method of Magnus series to Lie-algebraic equations originating in double-bracket flows. We show that the solution of the isospectral flow Y = [[Y; N ]; Y ], Y (0) = Y0 2 Sym(n), can be represented in the form Y (t) = e \Omega\Gamma Y0e , where the Taylor expansion of\Omega 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 finite `alphabet'. 1

Citations