Moser's theorem for hyperbolic-type degenerate lower tori in Hamiltonian system
The main result of the paper is about the existence of lower-dimensional tori for a class of degenerate Hamiltonian systems, that are also supposed to be only \(C^\ell\) smooth. This is a generalization of known results for which the degenerate case was considered within the analytic class, or the loss of analyticity was considered in the non-degenerate case. The proof is ruled out in the framework of KAM theory. The loss of regularity is overcome via the Jackson-Moser-Zehnder analytic approximation, while the degeneracy is treated through normal form theory for quasi-homogeneous polynomial systems and the stability of equilibrium points of odd degree polynomials. Some applications of the main theorem are given.
scientific article; zbMATH DE number 7382032
scientific article