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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2010, том 15, выпуск 2-3, страницы 300–318 (Mi rcd496)

Эта публикация цитируется в 1 статье

On the 75th birthday of Professor L.P. Shilnikov

Unique normal forms for area preserving maps near a fixed point with neutral multipliers

V. Gelfreicha, N. Gelfreikhb

a Mathematics Institute, University of Warwick, Zeeman Building, Coventry CV4 7AL, UK
b Faculty of Physics, St. Petersburg State University, Ulyanovskaya ul. 3, St. Petersburg, 198504, Russia

Аннотация: We study normal forms for families of area-preserving maps which have a fixed point with neutral multipliers $\pm 1$ at $\varepsilon=0$. 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.

Ключевые слова: area-preserving map, unique normal form, parabolic fixed point.

MSC: 37J40, 37G05, 70K45

Поступила в редакцию: 15.12.2009
Принята в печать: 29.12.2009

Язык публикации: английский

DOI: 10.1134/S1560354710020164



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