Unfoldings of quasi-periodic tori in reversible systems
It is well known that there exists a great similarity between Hamiltonian and reversible systems. In particular, \textit{J. Moser} [Stable and random motions in dynamical systems. Ann. Math. Stud. 77. Princeton, N. J.: Princeton University Press (1973; Zbl 0271.70009)] showed that the ``classical'' KAM-theorem on the persistence of a (maximal-dimensional) invariant quasi-periodic tori for perturbed Hamiltonian systems also holds in the reversible setting. In the paper a general KAM-theory for reversible systems is given. The cases of both maximal and lower- dimensional quasi-periodic invariant tori are investigated. By virtue of the fact that in some cases additional parameters are needed for the persistence of tori, an unfolding theory for reversible systems is developed.
scientific article; zbMATH DE number 740269
scientific article