论文标题
kolmogorov算法，用于等视汉密尔顿系统
Kolmogorov algorithm for isochronous Hamiltonian systems
论文作者
论文摘要
我们提出了一种类似Kolmogorov的算法，用于计算在“等级” Hamiltonian Systems中不变的圆环附近的正常形式，即具有$ \ Mathcal {h} = \ Mathcal = \ Mathcal {H} _0+\ varepsilon \ Mathcal \ Mathcal \ Mathcal \ Mathcal的hamiltonians的系统$ \ MATHCAL {H} _0 $是$ N $线性振荡器的哈密顿量，而$ \ Mathcal {H} _1 $可以作为振荡器规范变量中的多项式系列扩展。该方法可以被视为耦合振荡器的相应Lindstedt方法的正常形式类似物。我们在两个不同的方案下可能使用LindStedt方法本身的使用，即一种类似于Birkhoff正常形式方案的串联，而另一种类似于Kolomogorov的正常形式方案，在该方案中，我们预先修复了圆环的频率。
We present a Kolmogorov-like algorithm for the computation of a normal form in the neighborhood of an invariant torus in `isochronous' Hamiltonian systems, i.e., systems with Hamiltonians of the form $\mathcal{H}=\mathcal{H}_0+\varepsilon \mathcal{H}_1$ where $\mathcal{H}_0$ is the Hamiltonian of $N$ linear oscillators, and $\mathcal{H}_1$ is expandable as a polynomial series in the oscillators' canonical variables. This method can be regarded as a normal form analogue of a corresponding Lindstedt method for coupled oscillators. We comment on the possible use of the Lindstedt method itself under two distinct schemes, i.e., one producing series analogous to those of the Birkhoff normal form scheme, and another, analogous to the Kolomogorov normal form scheme in which we fix in advance the frequency of the torus.
