一类退化平面系统正规形计算.pdfVIP

Advances in Applied Mathematics 应用数学进展, 2016, 5(1), 98-111 Published Online February 2016 in Hans. /journal/aam /10.12677/aam.2016.51014 An Algorithm for Computing a Normal Form of a Class of Planar Degenerate Dynamical Systems Mengxiao Li, Tusen Huang Department of Mathematics, School of Sciences, Zhejiang Sci-Tech University, Hangzhou Zhejiang th th th Received: Feb. 4 , 2016; accepted: Feb. 19 , 2016; published: Feb. 26 , 2016 Copyright © 2016 by authors and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Abstract In this paper the normal forms of a class of planar degenerate dynamical systems are computed by using the method of Carleman linearlization, in the mean time, a sequence of the associated near identity change of variables is given. These results generalize the computations of normal forms for the non-degenerate dynamical systems with non-zero linear part in the classical theory of normal forms to those for the degenerate dynamical systems with zero linear part, and establish the bases to simplify the analyses of the dynamical properties of the degenerate systems. Keywords Planar Degenerate System, Normal Form, Near Identity Change of Variable, Method of Carleman Linearization 一类退化平面系统的正规形的计算 李梦晓，黄土森 浙江理工大学理学院数学系，浙江 杭州 收稿日期：2016年2月4 日；录用日期：2016年2月19 日；发布日期：2016年2月26 日 文章引用: 李梦晓, 黄土森. 一类退化平面系统的正规形的计算[J]. 应用数学进展, 2016, 5(1): 98-111. /10.12677/aam.2016.51014 李梦晓，黄土森 摘 要 本文利用Carleman线性化方法计算了一类平面退化系统的正规形，并给出相应的近恒等变量变换。这些 结果把经典正规形理论中只能计算具非零线性部分动力系统的正规形推广到可以计算具零线性部分系统 的正规形情形，为简化分析这类