## Reducibility of nonlinear differential equations to block-triangular form.(English. Russian original)Zbl 1031.34038

Russ. Math. 45, No. 6, 47-54 (2001); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2001, No. 6, 50-57 (2001).
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.

### MSC:

 34C20 Transformation and reduction of ordinary differential equations and systems, normal forms