On time sequences realizing characteristic and lower characteristic vectors of solutions (Q2703979)

The linear system NEWLINE\[NEWLINE \partial{x}/\partial{t_i}=A_i(t)x,\quad x\in \mathbb R^{n},\;t\in \mathbb R^{m}_{+},\;i=1,2,\dots ,m\geq 2,\;n\geq 1, \tag{1} NEWLINE\]NEWLINE with bounded continuously differentiable matrices \(A_i(t)\) satisfying the condition NEWLINE\[NEWLINE A_i(t)A_k(t)+\partial{A_i}/\partial{t_k}= A_k(t)A_i(t)+\partial{A_k}/\partial{t_i},\quad t\in \mathbb R^{m}_{+},\;i\neq k, NEWLINE\]NEWLINE for the complete integrability of (1) is considered. NEWLINENEWLINENEWLINEThe author proves a statement describing properties of the time sequences from \(\mathbb R^{m}_{+}\) used to evaluate characteristic and lower characteristic vectors of nontrivial solutions to (1).