2009/09/24 by Adriana Buică, Jaume Llibre, Buica, A. +3
Mathematics · Physics and Astronomy · #34C25 #34C29 #58F22 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.0909.4350
openalex publication_date 2009/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By a nondegenerate k-parameterized family K of periodic solutions we understand the situation when the geometric multiplicity of the multiplier +1 of the linearized on K system equals to k. Bifurcation of asymptotically stable periodic solutions from K is well studied in the literature and different conditions have been proposeddepending on whether the algebraic multiplicity of +1 is k or not (by Malkin, Loud, Melnikov, Yagasaki). In this paper we assume that the later is unknown. Asymptotic stability can not be understood in this case, but we demonstrate that the information about uniqueness of periodic solutions is still available. Moreover, we show that differentiability of the right hand sides is not necessary for the results of this kind and our theorems are proven under a kind of Lipschitz continuity.