Reducibility of nonlinear differential equations to block-triangular form (Q1599432)

The reducibility of nonlinear differential equations \[ \dot{x}=f(t,x), x \in\mathbb{R}^n, t \in\mathbb{R},\tag{1} \] in a group \(LG\) of Lyapunov's transformations is investigated. A sufficient condition for the reducibility of equation (1) to a block-triangular differential equation and a necessary and sufficient condition for the reducibility to a diagonal differential equation are obtained.