Exponential solutions of linear systems of differential equations whose coefficient matrix is skew symmetric
Irving J. Epstein · Proceedings of the American Mathematical Society · 1966
been thoroughly investigated, namely when A and E are both constant matrices. Of much greater interest, however, are the cases where E or A represent a given set of matrices depending on one or several parameters, as for instance when E represents an arbitrary element of a Lie group. In these cases great difficulties arise if a global solution (for all values of the parameters) is sought for E — exp A, where either E or A are given and the other one has to be found. Some of the difficulties encountered are, for instance, described in [l] and [2]. A basic reason for these difficulties is that the eigenvalues of a matrix E(t) depending analytically on one parameter t are, in general, not analytic functions of / (as, for instance, in the case of m G -D