A Lie bracket decomposition and its application to flows on symmetric matrices (Q1200563)

The paper deals with the differential equations of the form (1): \(\dot X(t)=[X(t),A(t)]+B(t)\), where \(X(t)\) is a symmetric matrix and \(A(t)\) is a skew-symmetric matrix. The paper is motivated by the observation that the form of the differential equation (1) is not unique. For example, the flow \(X(t)\) given by (1) also satisfies the equation \(\dot X(t)=[X(t),\tilde A(t)]+B(t)\), where \(\tilde A(t)=A(t)+m(t)X(t)\), for any function \(m(t)\). The purpose of this paper is to present such choice of the conditions which must be imposed on \(A(t)\), \(B(t)\) to obtain uniqueness.