Ergodic perturbations of degenerate integrable Hamiltonian systems

A. B. Katok

Izvestiya. Mathematics , Tome 7 (1973) no. 3, pp. 535-571.

Résumé

Hamiltonian systems arbitrarily close in the $C^r$ topology $(r=1,2,\dots)$ to a given integrable degenerate Hamiltonian system of class $C^\infty$ 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.

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