Quasiperiodic Poincare Persistence at High Degeneracy

2021/11/23 by Qian, Weichao, Li, Yong, Yang, Xue
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2111.11619

Abstract

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

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• Lower dimensional invariant tori for multi-scale Hamiltonian systems
• Persistence of lower dimensional invariant tori on sub-manifolds in Hamiltonian systems
• Melnikov's persistence for completely degenerate Hamiltonian systems
• A simple proof of the invariant torus theorem
• Degenerate elliptic resonances