Self-similar flows
The semi-similar flows studied in the paper arise from a matrix differential equation \(\dot B=[B,C]\) where \(C=C(t,B)\). The problem is related to the problem of FG-decomposition: if \({\mathcal F}\), \({\mathcal G}\) are two closed subgroups of the general linear group \(GL_ n(F)\) \((F=R\) or C) with \({\mathcal F}\cap {\mathcal G}=\{I\},\) express \(A\in GL_ n(P)\) as a product FG where \(F\in {\mathcal F}\), \(G\in {\mathcal G}\). FG-algorithm: starting from a given matrix \(A\in GL_ n(F)\), introduce the sequence: \(A_ 0=A,A_ 1,A_ 2,..\). as follows: \(A_ i=\bar F_{i+1}\bar G_{i+1},\) \(A_{i+1}=\bar G_{i+1}\bar F_{i+1}.\) There exists a continuous version of this algorithm. The authors consider flows associated with different \({\mathcal F}\) and \({\mathcal G}\), using some results from the theory of Lie groups and algebras.
scientific article; zbMATH DE number 4089724
scientific article