Quasiperiodic Poincaré persistence at high degeneracy

For Hamiltonian systems with high-order degenerate perturbation, we study the persistence of resonant invariant tori, where the resonant tori might be elliptic, hyperbolic or mixed types. As a consequence, we prove a quasiperiodic Poincare theorem at high degeneracy. This answers a long standing conjecture on the persistence of resonant invariant tori in general situations.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we investigate the persistence of resonant invariant tori in Hamiltonian systems with high-order degenerate perturbation, and prove a quasiperiodic Poincare theorem under high degeneracy, answering a long-standing conjecture on the persistence of resonant invariant tori in general situations.