Ergodic perturbations of degenerate integrable hamiltonian systems

Hamiltonian systems arbitrarily close in the Cr topology (r= 1, 2, …) to a given integrable degenerate Hamiltonian system of class C which generate an ergodic flow on each manifold of constant energy are constructed. Applications: Small perturbations of a system generated by independent oscillators and Finsler metrics close to standard Riemannian metrics on symmetric spaces of rank 1.