On the Baire classification of positive characteristic exponents in the Perron effect of change of their values (Q1731301)

The main result reads as follows. Assume that all nontrivial solutions $y(t,t_0)$ of the system $\dot{y}=F(t,y)$, where $y\in\mathbb{R}^n$, $F$ is continuously differentiable with respect to its arguments, and satisfies $F(t,0)\equiv 0$, are infinitely extendible and have finite characteristic exponents. Then the characteristic exponent $\lambda[y(\cdot,y_0)]$ of these solutions is a function of the second Baire class of their initial vectors $y_0\in\mathbb{R}^n\setminus\{0\}$.