Degenerate resonances and their stability in planar systems with small negative divergence

2011/12/17 by Oleg Makarenkov, O. Yu. Makarenkov, Makarenkov, O. Yu. +2
Mathematics · Physics and Astronomy · #34C25 (Primary) 34D10 (Secondary) #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Quantum chaos and dynamical systems #math.DS #msc:34C25 #msc:34D10

paper · pdf · doi:10.48550/arxiv.1112.4075

5 pages

arxiv created 2011/12/17 · openalex publication_date 2011/12/17 · arxiv updated 2011/12/20 · openalex created_date 2016/09/23 · openalex updated_date 2026/07/28

Abstract

We consider a conservative system with small periodic perturbations under the assumption that the divergence of the perturbed system is negative. The main theorems provide universal sufficient conditions for the existence and asymptotic stability of periodic solutions that apply regardless of whether the zeros of the bifurcation function are simple or not.

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