Quasiperiodic Poincare Persistence at High Degeneracy

Abstract

For Hamiltonian systems with degeneracy of any higher order, we study the persistence of resonant invariant tori, which as some lowerdimensional invariant tori might be elliptic, hyperbolic or of mixed types. Hence we prove a quasiperiodic Poincaré theorem at high degeneracy. This answers a long standing conjecture on the persistence of resonant invariant tori in quite general situations.