Gelfreich, Vassili and Gelfreikh, N.. (2010) Unique normal forms for area preserving maps near a fixed point with neutral multipliers. Regular and Chaotic Dynamics, Vol.15 (No.2-3). pp. 300-318. ISSN 1560-3547

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Abstract

We study normal forms for families of area-preserving maps which have a fixed point with neutral multipliers +/- 1 at E > = 0. Our study covers both the orientation-preserving and orientation-reversing cases. In these cases Birkhoff normal forms do not provide a substantial simplification of the system. In the paper we prove that the Takens normal form vector field can be substantially simplified. We also show that if certain non-degeneracy conditions are satisfied no further simplification is generically possible since the constructed normal forms are unique. In particular, we provide a full system of formal invariants with respect to formal coordinate changes.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery Q Science > QC Physics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Regular and Chaotic Dynamics
Publisher:	M A I K Nauka - Interperiodica
ISSN:	1560-3547
Date:	June 2010
Volume:	Vol.15
Number:	No.2-3
Number of Pages:	19
Page Range:	pp. 300-318
Identification Number:	10.1134/S1560354710020164
Status:	Peer Reviewed
Publication Status:	Published
Funder:	Royal Society (Great Britain)
URI:	http://wrap.warwick.ac.uk/id/eprint/5983

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