Birkhoff normal form的收敛有时意味着归一化变换的收敛
Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation
摘要：
考虑一个解析哈密顿系统在其频率为零的解析不变环面$\mathcal T_0$附近.我们假设在$\mathcal T_0$上的哈密顿量的Birkhoff标准形是收敛的，并且有一个特殊的形式：它是它的非退化二次部分的一个解析函数。我们证明，在这种情况下，有一个分析的正则变换-而不仅仅是一个正式的幂级数-使其伯克霍夫正规形式的哈密顿量。
英文摘要：
Consider an analytic Hamiltonian system near its analytic invariant torus $\mathcal T_0$ carrying zero frequency. We assume that the Birkhoff normal form of the Hamiltonian at $\mathcal T_0$ is convergent and has a particular form: it is an analytic function of its non-degenerate quadratic part. We prove that in this case there is an analytic canonical transformation -- not just a formal power series -- bringing the Hamiltonian into its Birkhoff normal form.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
