The Baire class of minorants of Lyapunov’s exponents. (English. Russian original) Zbl 1052.34056

Bykov, V. V.; Salov, E. E.

Mosc. Univ. Math. Bull. 58, No. 1, 36-43 (2003); translation from Vestn. Mosk. Univ., Ser. I 2003, No. 1, 33-40 (2003).

The authors show that the maximal lower semicontinuous (in the uniform topology) minorant of the intermediate Lyapunov exponent of the linear system \[ \dot x = A(t)x, \quad x\in \mathbb{R}^n,\quad t\in \mathbb{R}^+, \] with operator-function \(A\) piece-wise continuous and bounded on the half-line \(\mathbb{R}^+\) belongs to the third Baire class in compact open topology.

Reviewer: A. A. Martynyuk (Kyïv)

MSC:

34D08	Characteristic and Lyapunov exponents of ordinary differential equations
34A30	Linear ordinary differential equations and systems

Keywords:

linear system; intermediate Lyapunov exponent