Unique normal forms for area preserving maps near a fixed point with neutral multipliers
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 1560-3547Full text not available from this repository.
Official URL: http://dx.doi.org/10.1134/S1560354710020164
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|
|Official Date:||June 2010|
|Number of Pages:||19|
|Page Range:||pp. 300-318|
|Funder:||Royal Society (Great Britain)|
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