Unique normal forms for the Takens-Bogdanov singularity in a special case

Xiaofeng Wang; Guoting Chen; Duo Wang

doi:10.1016/S0764-4442(01)01869-9

Unique normal forms for the Takens-Bogdanov singularity in a special case

Translated title of the contribution: Unicité des formes normales pour la singularité de Takens-Bogdanov dans un cas particulier

Xiaofeng Wang^*
, Guoting Chen
, Duo Wang

^*Corresponding author for this work

Tsinghua University
Université de Lille
Peking University

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

Abstract

We consider further reduction of normal forms for nilpotent planar vector fields. We give a unique normal form for a special case of an open problem for the Takens-Bogdanov singularity.

Translated title of the contribution	Unicité des formes normales pour la singularité de Takens-Bogdanov dans un cas particulier
Original language	French
Pages (from-to)	551-555
Number of pages	5
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	332
Issue number	6
DOIs	https://doi.org/10.1016/S0764-4442(01)01869-9
Publication status	Published - 15 Mar 2001
Externally published	Yes

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10.1016/S0764-4442(01)01869-9

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title = "Unique normal forms for the Takens-Bogdanov singularity in a special case",

abstract = "We consider further reduction of normal forms for nilpotent planar vector fields. We give a unique normal form for a special case of an open problem for the Takens-Bogdanov singularity.",

author = "Xiaofeng Wang and Guoting Chen and Duo Wang",

note = "Funding Information: Acknowledgements. This paper was prepared when D. Wang was visiting the University of Lille-1 and X. Wang was visiting Le Laboratoire AGAT, UMR 8524 du CNRS, at the same university. They appreciate the hospitality of the Department of Mathematics at the University of Lille-1. X. Wang is supported by NSF of China and the Basic Research Foundation of Tsinghua University (project 98JC071). D. Wang is supported by NSF of China and NSF of Beijing.",

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AU - Chen, Guoting

AU - Wang, Duo

N1 - Funding Information: Acknowledgements. This paper was prepared when D. Wang was visiting the University of Lille-1 and X. Wang was visiting Le Laboratoire AGAT, UMR 8524 du CNRS, at the same university. They appreciate the hospitality of the Department of Mathematics at the University of Lille-1. X. Wang is supported by NSF of China and the Basic Research Foundation of Tsinghua University (project 98JC071). D. Wang is supported by NSF of China and NSF of Beijing.

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N2 - We consider further reduction of normal forms for nilpotent planar vector fields. We give a unique normal form for a special case of an open problem for the Takens-Bogdanov singularity.

AB - We consider further reduction of normal forms for nilpotent planar vector fields. We give a unique normal form for a special case of an open problem for the Takens-Bogdanov singularity.

UR - https://www.scopus.com/pages/publications/0011957788

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DO - 10.1016/S0764-4442(01)01869-9

M3 - 文章

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SN - 0764-4442

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EP - 555

JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

IS - 6

ER -

Unique normal forms for the Takens-Bogdanov singularity in a special case

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