Varieties and analytic normalizations of partially integrable systems

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• 作者：Zengji Du^a ; ^{zjdu@jsnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Valery G. Romanovski^b ; ^{valery.romanovsky@uni-mb.si" class="auth_mail" title="E-mail the corresponding author} ; Xiang Zhang^c ; ^{xzhang@sjtu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 34A25 ; 34C20 ; secondary ; 34C05 ; 34C41 ; 34A34
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 May 2016
• 年：2016
• 卷：260
• 期：9
• 页码：6855-6871
• 全文大小：310 K

文摘

For analytic differential systems $\dot{x}=Ax+f(x)$ in Fⁿ${\mathbb{F}}^n$ with F=R$\mathbb{F}=\mathbb{R}$ or C$\mathbb{C}$, we study the varieties of their partial integrability in a neighborhood of the origin. We also prove the existence of analytic normalizations of partially integrable differential systems.