A GENERAL AVERAGING METHOD FOR AFFINE PERIODIC SOLUTIONS  

作　　者：Xue YANG Jiamin XING Yong LI 杨雪;邢佳敏;李勇(College of Mathematics,Jilin University,Changchun 130012,China;School of Mathematics and Statistics,and Center for Mathematics and Interdisciplinary Sci Northeast Normal University,Changchun 130024,China)

机构地区：[1]College of Mathematics,Jilin University,Changchun 130012,China [2]School of Mathematics and Statistics,and Center for Mathematics and Interdisciplinary Sciences Northeast Normal University,Changchun 130024,China

出　　处：《Acta Mathematica Scientia》2024年第6期2207-2224,共18页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(12371191;12071175);supported by the NSFC(12071175;11901080);supported by the NSFC(12071175);the Fundamental Research Funds For the Central Universities(2412023YQ003);the Natural Science Foundation of Jilin Province(20200201253JC)。

摘　　要：We consider the persistence of affine periodic solutions for perturbed affine periodic systems.Such(Q,T)-affine periodic solutions have the form x(t+T)=Qx(t)for all t∈R,where T>0 is fixed and Q is a nonsingular matrix.These are a kind of spatiotemporal symmetric solutions,e.g.spiral waves.We give the averaging method for the existence of affine periodic solutions in two situations:one in which the initial values of the affine periodic solutions of the unperturbed system form a manifold,and another that does not rely on the structure of the initial values of the unperturbed system's affine periodic solutions.The transversal condition is determined using the Brouwer degree.We also present a higher order averaging method for general degenerate systems by means of the Brouwer degree and a Lyapunov-Schmidt reduction.

关 键 词：affine-periodic solution perturbed system Brouwer degree averaging method 

分 类 号：O175[理学—数学]