Naudot, Vincent and Yang, Jia Zhong (2008) On the index of finite determinacy of vector fields with resonances. Acta Mathematica Sinica, Volume 24 (Number 8). pp. 1401-1408. doi:10.1007/s10114-008-7073-8 ISSN 1439-8516.

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Abstract

In this paper we study normal forms for a class of germs of 1-resonant vector fields on R-n with mutually different eigenvalues which may admit extraneous resonance relations. We give an estimation on the index of finite determinacy from above as well as the essentially simplified polynomial normal forms for such vector fields. In the case that a vector field has a zero eigenvalue, the result leads to an interesting corollary, a linear dependence of the derivatives of the hyperbolic variables on the central variable.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Normal forms (Mathematics), Vector fields, Finite fields (Algebra), Resonance
Journal or Publication Title:	Acta Mathematica Sinica
Publisher:	Springer
ISSN:	1439-8516
Official Date:	August 2008
Dates:	Date Event August 2008 Published
Volume:	Volume 24
Number:	Number 8
Number of Pages:	8
Page Range:	pp. 1401-1408
DOI:	10.1007/s10114-008-7073-8
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Grant number:	NSFC-10571002

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