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Article Dans Une Revue Dynamical Systems Année : 2023

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

Résumé

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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Dates et versions

hal-01969255 , version 1 (03-01-2019)
hal-01969255 , version 2 (10-02-2019)
hal-01969255 , version 3 (15-11-2021)
hal-01969255 , version 4 (03-04-2022)

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W. Oukil. Ordinary differential equations defined by a trigonometric polynomial field: Behavior of the solutions. Dynamical Systems, In press, pp.1-19. ⟨10.1080/14689367.2023.2170212⟩. ⟨hal-01969255v4⟩

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