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Unique normal forms for area preserving maps near a fixed point with neutral multipliers
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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. doi:10.1134/S1560354710020164 ISSN 1560-3547.
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Official URL: http://dx.doi.org/10.1134/S1560354710020164
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 | ||||
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Subjects: | Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery Q Science > QC Physics |
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Regular and Chaotic Dynamics | ||||
Publisher: | M A I K Nauka - Interperiodica | ||||
ISSN: | 1560-3547 | ||||
Official Date: | June 2010 | ||||
Dates: |
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Volume: | Vol.15 | ||||
Number: | No.2-3 | ||||
Number of Pages: | 19 | ||||
Page Range: | pp. 300-318 | ||||
DOI: | 10.1134/S1560354710020164 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Funder: | Royal Society (Great Britain) |
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