Residues of Destructed Resonance Torus

In this paper, we propose a method to handle the problem of complete degeneracy in the study of lower dimensional invariant tori surviving from destructed resonant torus. As its application, we obtain a different proof of the existence of co-dimension one invariant tori. No other condition is assumed on the perturbation except for the smallness.

Automated summary

In this paper, a method is proposed to address the complete degeneracy problem in lower dimensional invariant tori surviving from destructed resonant torus. As an application, a different proof of the existence of co-dimension one invariant tori is obtained, with no additional assumptions on the perturbation other than its smallness.