耦合振子的代数度

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-08-22 DOI:10.1016/j.aim.2025.110492

Paul Breiding , Mateusz Michałek , Leonid Monin , Simon Telen

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引用次数: 0

摘要

近似耦合Duffing方程的周期解相当于求解一个多项式方程组。复数解的数量衡量了这个近似问题的代数复杂性。利用Khovanskii基理论，我们证明了这个数是由多面体的体积给出的。我们还展示了如何使用数值非线性代数计算所有解。

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The algebraic degree of coupled oscillators

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 polytope. We also show how to compute all solutions using numerical nonlinear algebra.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.