Characteristic spectrum for differential systems (Q1268571)

The characteristic spectrum of the tangent map induced by a \(C^1\)-vector field on a compact smooth manifold \(M^n\) is studied. It is proved that this spectrum can be expressed by the integrals of the qualitative functions with respect to ergodic measures over the bundle of orthonormal \(n\)-frames. Analogously, the characteristic spectrum of the parallelotope cocycle of the differential system is expressed by integrals of the qualitative function of \(M^n\) with respect to ergodic measures over \(M^n\).