A New KAM Theorem for the Hyperbolic Lower Dimensional Tori in Reversible Systems

This paper puts forward a new KAM theorem for the hyperbolic lower dimensional tori in reversible system without assuming any non-degeneracy condition, which can be viewed as a unified form under all kinds of non-degenerate conditions, including Kolmogorov, Bruno and Russmann non-degeneracy condition. The theorem with some non-degeneracy conditions not only includes many previous achievements on KAM theory in reversible systems, but also gives some interesting results on the persistence of hyperbolic lower dimensional invariant tori with prescribed frequency in reversible system.