论文标题
耦合振荡器的代数程度
The Algebraic Degree of Coupled Oscillators
论文作者
论文摘要
耦合行程的近似周期解决方案等于求解多项式方程系统。复杂解决方案的数量测量了此近似问题的代数复杂性。使用Khovanskii碱基的理论，我们表明该数字由某个多层的体积给出。我们还展示了如何使用数值非线性代数计算所有解决方案。
Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of Khovanskii bases, we show that this number is given by the volume of a certain polytope. We also show how to compute all solutions using numerical nonlinear algebra.
