群S₄对称高维自治系统的Hopf分岔

群S 4 对称高维自治系统的Hopf分岔 Hopf Bifurcation for Autonomous System in Presence of Group S 4 Symmetry 陈士华 CHEN Shi\|hua 1 first-author 曾宪武 ZENG Xian\|wu 1 丰建文 FENG Jian\|wen 1 武汉大学数学科学学院,湖北,武汉,430072 武汉大学数学科学学院,湖北,武汉,430072 School of Mathematical Science, Wuhan University School of Mathematical Science, Wuhan University 研究群对称高维自治系统的Hopf分岔 .利用Lyapunov Schmidt方法得到分岔问题的约化映射 ,讨论约化映射的对称性和不变子空间 ,由此导出分岔方程 ,利用分岔方程不仅研究了Hopf分岔解的对称结构 ,而且得到了Hopf分岔产生的条件 . Hopf bifurcation for autonomous system in presence of Group symmetry is studied. The reduced map of Hopf bifurcation is established by making use of Lyapunov\|Schmidt method, its symmetry properties and invariant subspaces are discussed as well.All above results lead up to the bifurcation equation.In the end, both the symmetry structures of Hopf bifurcation solution and the existence condition for Hopf bifurcation are obtained from the bifurcation equation. 群对称 自治系统 Hopf分岔 group symmetry autonomous system Hopf bifurcation O175 国家自然科学基金!（1 9531 0 70 ）;湖北省自然科学基金!资助项目 （98J1 2 1 ） 2001-01-01 2021-04-01 1