Analytic invariants of dynamic systems with positive entropy (Q1280377)

The author studies a dynamical system given by the vector field \(v(x)\) on a three-dimensional compact manifold \(M\). It is assumed that the metric entropy of the flow \(g^t_v\) is positive with respect to the measure prescribed by the volume form being invariant with respect to \(g^t_v\) and induced by some metric. Restrictions are investigated on the existence of various invariants of the dynamical system. The case of Hamiltonian systems is discussed.