标题：Almost-periodic bifurcations for one-dimensional degenerate vector fields
作者：Si W.; Xu X.; Si J.
作者机构：[Si, W] School of Mathematics, Shandong University, Jinan, China;[ Xu, X] School of Mathematics, Shandong University, Jinan, China;[ Si, J] School of 更多
通讯作者地址：[Si, J] School of Mathematics, Shandong UniversityChina;
关键词：Almost-periodic bifurcations; KAM theory; Pöschel–Rüssmann KAM method; singularity theory; universal unfolding
摘要：Quasi-periodic high order degenerate bifurcation theories have been well established, but works which are related to almost-periodic bifurcations seem to be very few. In this paper, we consider the almost-periodic time-dependent perturbations of one-dimensional degenerate vector field (Formula presented.) With the KAM theory and singularity theory, we show that the universal unfolding of the vector field can persist under small almost-periodic perturbation if some appropriate non-resonant conditions are satisfied, which implies strongly non-resonant invariant tori in the integrable part and all bifurcation scenario can survive under any small almost-periodic perturbation. © 2019, © 2019 Informa UK Limited, trading as Taylor & Francis Group.