Unique normal forms for nilpotent planar vector fields

Guoting Chen; Duo Wang; Xiaofeng Wang

doi:10.1142/S0218127402005741

Unique normal forms for nilpotent planar vector fields

Guoting Chen^*
, Duo Wang
, Xiaofeng Wang

^*Corresponding author for this work

Université de Lille
Peking University
Tsinghua University

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

20 Citations (Scopus)

Abstract

Further reduction of normal forms for nilpotent planar vector fields has been considered. Unique normal form for a special case of an unsolved problem for the Takens-Bogdanov singularity is given. Computations in Maple are used to conjecture the main results and some computations in the proof are also done with Maple.

Original language	English
Pages (from-to)	2159-2174
Number of pages	16
Journal	International Journal of Bifurcation and Chaos
Volume	12
Issue number	10
DOIs	https://doi.org/10.1142/S0218127402005741
Publication status	Published - Oct 2002
Externally published	Yes

Keywords

Linear grading
Nilpotent vector field
Normal form

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10.1142/S0218127402005741

Cite this

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title = "Unique normal forms for nilpotent planar vector fields",

abstract = "Further reduction of normal forms for nilpotent planar vector fields has been considered. Unique normal form for a special case of an unsolved problem for the Takens-Bogdanov singularity is given. Computations in Maple are used to conjecture the main results and some computations in the proof are also done with Maple.",

keywords = "Linear grading, Nilpotent vector field, Normal form",

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

note = "Funding Information: This work is partially supported by NSF of China and NSF of Beijing for D. Wang, and by the National Key Basic Research Special Fund under grant number G1998020309 for X. Wang.",

year = "2002",

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AU - Chen, Guoting

AU - Wang, Duo

AU - Wang, Xiaofeng

N1 - Funding Information: This work is partially supported by NSF of China and NSF of Beijing for D. Wang, and by the National Key Basic Research Special Fund under grant number G1998020309 for X. Wang.

PY - 2002/10

Y1 - 2002/10

N2 - Further reduction of normal forms for nilpotent planar vector fields has been considered. Unique normal form for a special case of an unsolved problem for the Takens-Bogdanov singularity is given. Computations in Maple are used to conjecture the main results and some computations in the proof are also done with Maple.

AB - Further reduction of normal forms for nilpotent planar vector fields has been considered. Unique normal form for a special case of an unsolved problem for the Takens-Bogdanov singularity is given. Computations in Maple are used to conjecture the main results and some computations in the proof are also done with Maple.

KW - Linear grading

KW - Nilpotent vector field

KW - Normal form

UR - https://www.scopus.com/pages/publications/0036816543

U2 - 10.1142/S0218127402005741

DO - 10.1142/S0218127402005741

M3 - Article

AN - SCOPUS:0036816543

SN - 0218-1274

VL - 12

SP - 2159

EP - 2174

JO - International Journal of Bifurcation and Chaos

JF - International Journal of Bifurcation and Chaos

IS - 10

ER -

Unique normal forms for nilpotent planar vector fields

Abstract

Keywords

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