On the Baire Classification of Positive Characteristic Exponents in the Perron Effect of Change of Their Values
N. A. Izobov, А. В. Ильин · Differential Equations · 2018
In the complete Perron effect of change of values of characteristic exponents, where all nontrivial solutions y ( t , y 0 ) of the perturbed two-dimensional differential system are infinitely extendible and have finite positive exponents (the exponents of the linear approximation system being negative), we prove that the Lyapunov exponent λ [ y (·, y 0 )] of these solutions is a function of the second Baire class of their initial vectors y 0 ∈ ℝ n {0}.