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	Further reduction of normal forms and unique normal forms of smooth maps
	Wang, Duo ; Zheng, Min ; Peng, Jianping
	2008
关键词	normal form recursive formula further reduction infinite order normal form unique normal form SIMPLEST NORMAL FORMS NEIMARK-SACKER BIFURCATIONS VECTOR-FIELDS HOPF SINGULARITIES
英文摘要	Further reduction for classical normal forms of smooth maps is considered in this paper. Firstly, based on the idea of computation of simplest normal forms for vector fields [Yu & Yuan, 2003], we compute the transformed map of a given smooth map under a near identity formal transformation, and give a recursive formula for the homogeneous terms of the transformed map, which is a powerful tool for further reduction of classical normal forms of smooth maps. Secondly, by using the recursive formula, the idea of [Chen & Della Dora, 1999] for further reduction of normal forms for maps and the method introduced by Kokubu et al. [1996] for further reduction of normal forms of vector. elds, we develop the concepts of Nth order normal forms and in. nite order normal forms of smooth maps, and give some sufficient conditions for uniqueness of normal forms of smooth maps. As an application, we show the occurrence of the flip-Neimark-Sacker bifurcation in a financial model.; http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000257292200012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=8e1609b174ce4e31116a60747a720701 ; Mathematics, Interdisciplinary Applications; Multidisciplinary Sciences; SCI(E); EI; 2; ARTICLE; 3; 803-825; 18
语种	英语
出处	SCI ; EI
出版者	international journal of bifurcation and chaos
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/314892]
专题	数学科学学院
推荐引用方式 GB/T 7714	Wang, Duo,Zheng, Min,Peng, Jianping. Further reduction of normal forms and unique normal forms of smooth maps. 2008-01-01.

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