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

2019/01/04 by Walid OUKIL, Oukil, W
Computer Science · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1901.01016

openalex publication_date 2019/01/04 · openalex created_date 2019/01/11 · openalex updated_date 2026/07/28

Abstract

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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