Unique orbital normal form for vector fields of hopf-zero singularity

Guoting Chen; Duo Wang; Jiazhong Yang

doi:10.1007/s10884-005-2876-0

Unique orbital normal form for vector fields of hopf-zero singularity

Guoting Chen, Duo Wang^*, Jiazhong Yang

^*Corresponding author for this work

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

14 Citations (Scopus)

Abstract

Normal forms for vector fields of Hopf-zero singularity in R ³ are studied. Multiple Lie bracket method is used to give unique normal forms under both conjugacy and orbital equivalence for such vector fields with a generic quadratic part.

Original language	English
Pages (from-to)	3-20
Number of pages	18
Journal	Journal of Dynamics and Differential Equations
Volume	17
Issue number	1
DOIs	https://doi.org/10.1007/s10884-005-2876-0
Publication status	Published - Jan 2005
Externally published	Yes

Keywords

Conjugacy
Orbital equivalence
Unique normal forms
Vector fields

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10.1007/s10884-005-2876-0

Cite this

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title = "Unique orbital normal form for vector fields of hopf-zero singularity",

abstract = "Normal forms for vector fields of Hopf-zero singularity in R 3 are studied. Multiple Lie bracket method is used to give unique normal forms under both conjugacy and orbital equivalence for such vector fields with a generic quadratic part.",

keywords = "Conjugacy, Orbital equivalence, Unique normal forms, Vector fields",

author = "Guoting Chen and Duo Wang and Jiazhong Yang",

note = "Funding Information: GC appreciates the hospitality of the Institute of Mathematics in Peking University where this work was started. JY is grateful for the hospitality of Universit{\'e} de Lille 1 when he visited there. DW and JY are partially supported by NSFC(10271007), RFDP(20010001042) and NSFC(10271006), respectively.",

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doi = "10.1007/s10884-005-2876-0",

language = "English",

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AU - Chen, Guoting

AU - Wang, Duo

AU - Yang, Jiazhong

N1 - Funding Information: GC appreciates the hospitality of the Institute of Mathematics in Peking University where this work was started. JY is grateful for the hospitality of Université de Lille 1 when he visited there. DW and JY are partially supported by NSFC(10271007), RFDP(20010001042) and NSFC(10271006), respectively.

PY - 2005/1

Y1 - 2005/1

N2 - Normal forms for vector fields of Hopf-zero singularity in R 3 are studied. Multiple Lie bracket method is used to give unique normal forms under both conjugacy and orbital equivalence for such vector fields with a generic quadratic part.

AB - Normal forms for vector fields of Hopf-zero singularity in R 3 are studied. Multiple Lie bracket method is used to give unique normal forms under both conjugacy and orbital equivalence for such vector fields with a generic quadratic part.

KW - Conjugacy

KW - Orbital equivalence

KW - Unique normal forms

KW - Vector fields

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U2 - 10.1007/s10884-005-2876-0

DO - 10.1007/s10884-005-2876-0

M3 - Article

AN - SCOPUS:23044491410

SN - 1040-7294

VL - 17

SP - 3

EP - 20

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

IS - 1

ER -

Unique orbital normal form for vector fields of hopf-zero singularity

Abstract

Keywords

Access to Document

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