Quasi-periodic solutions for differential equations with an elliptic-type degenerate equilibrium point under small perturbations

2017/10/03 by Xuemei Li, Li, Xuemei, Zaijiu Shang +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.1710.01181

32pages

arxiv created 2017/10/03 · arxiv updated 2017/10/04

Abstract

This work focuses on the existence of quasi-periodic solutions for ordinary and delay differential equations (ODEs and DDEs for short) with an elliptic-type degenerate equilibrium point under quasi-periodic perturbations. We prove that under appropriate hypotheses there exist quasi-periodic solutions for perturbed ODEs and DDEs near the equilibrium point for most parameter values, then apply these results to the delayed van der Pol's oscillator with zero-Hopf singularity.

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