Lyapunov exponents of linear extensions of a dynamic system on a torus (Q1076884)

The author considers the dynamic system \[ f^ tw=(w_ 1+t\omega_ 1(mod 1),...,w_ m+t\omega_ m(mod 1)) \] on the torus \(T^ m\), where \(\omega_ 1,...,\omega_ m\) is a fixed set of real numbers rationally independent, and defines the system \(x'=A(f^ tw)x,\) where \(x\in R^ n\), \(A\in L_ 1(T^ m;Hom(R^ n,R^ n)),\) \(w\in T^ m\). The Lyapunov exponents of this system are discontinuous functions of A. The paper describes their behaviour near the points of discontinuity and the set of points of continuity.