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arXiv · 1901.01016

Ordinary differential equations defined by a trigonometric polynomial field: Behavior of the solutions

W Oukil
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Abstract

We consider the ordinary differential equations defined by a trigonometric polynomial field, we prove that any solution $x$ admits a "rotation vector" $\rho\in \mathbb{R}^n$. More precisely, the function $t\mapsto x(t)-\rho t$ is bounded on time and it is a "weak almost periodic" function of "slope" $\rho$.

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W Oukil. 2019-01-04. Ordinary differential equations defined by a trigonometric polynomial field: Behavior of the solutions. https://doi.org/10.1080/14689367.2023.2170212

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