document: On the discretization of double-bracket flows 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 ' = -LSB- -LSB- Y , N -RSB- , Y -RSB- , Y -LRB- O -RRB- = Y/sub 0 / in Sym -LRB- n -RRB- , can be represented in the form Y -LRB- t -RRB- = e/sup Omega -LRB- t -RRB- / Y/sub 0/e/sup - Omega -LRB- 1 -RRB- / , where the Taylor expansion of Omega can be constructed explicitly , term-by-term , identifying individual expansion terms with certain rooted trees with bicolor leaves . This approach is extended to other Lie-algebraic equations that can be appropriately expressed in terms of a finite `` alphabet ''
doc_bio_tags: O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: magnus series isospectral flow taylor expansion bicolor leaves
abstractive_keyphrases: double-bracket flows discretization lie-algebraic equations