| Volume 14, Number 6, 2024, Pages - DOI：10.11948/JAAC-2023-0503 |
| The existence of response tori for Hamiltonian with normal degeneracy |
| Lu Xu,Wen Si,Mengmeng Wu |
| Keywords:Normal degeneracy, KAM theory, response solution |
| Abstract: |
| Most of the previous results focus on a single oscillator equation and prove the existences
of response solutions under certain non-degenerate assumptions. In the present paper, we
will consider high dimensional system coupled by oscillator equations in different degenerate type.
We will prove that the response solutions still exist around perturbed equilibria, which reveals the mechanics
of the existence of response solution for a system coupled by degenerate nonlinear oscillator equations.
For the sake of generality, we will actually consider a general Hamiltonian normal form
and prove the persistence of invariant tori with fixed Diophantine frequency $\omega$
by the methods of finding relative equilibria, improving the order of perturbations, KAM iterations, and measure estimates.
The general result will then be applied to the problem of the existence of
response solutions of the coupled system. |
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