On lower dimensional invariant tori in reversible systems

In this paper, a result on the persistence of lower dimensional invariant tori in reversible systems is obtained under some weak non-degenerate conditions. Such a result can be applied to the case where normal frequencies are not simple and some of them may be zero. We also give an answer of a conjecture of M. B. Sevryuk (1986, "Reversible Systems," Lecture Notes in Math.. Vol. 1211, Springer-Verlag, New York/Berlin) about the existence of lower-dimensional invariant tori in resonant zones. (C) 2001 Academic Press.