What is it about?
We consider the ordinary differential equations defined by a trigonometric polynomial field, we prove that any solution x admits a "rotation vector" ρ∈Rn. More precisely, the function t↦x(t)−ρt is bounded on time and it is a "weak almost periodic" function of "slope" ρ.
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Why is it important?
The article solves a long-standing problem concerning the Kuramoto model in particular and periodic systems in general, namely to prove that the long-term average frequencies exist for an oscillator network. See this article and in particular equation (4): https://academic.oup.com/ptp/article/77/5/1005/1854307
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This page is a summary of: Ordinary differential equations defined by a trigonometric polynomial field: behaviour of the solutions, Dynamics and Stability of Systems, February 2023, Taylor & Francis,
DOI: 10.1080/14689367.2023.2170212.
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