UNIQUE NORMAL FORMS FOR NILPOTENT PLANAR VECTOR FIELDS-Reference-Cited by-同舟云学术

UNIQUE NORMAL FORMS FOR NILPOTENT PLANAR VECTOR FIELDS

Published:2002-10 Issue:10 Volume:12 Page:2159-2174
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

CHEN GUOTING¹,WANG DUO²,WANG XIAOFENG³

Affiliation:

1. UFR de Mathématiques, Université de Lille 1, 59655 Villeneuve d'Ascq, France

2. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

3. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127402005741

Reference23 articles.

1. Geometrical Methods in the Theory of Ordinary Differential Equations

2. Unique normal forms for vector fields and Hamiltonians

3. Further reduction of the Takens-Bogdanov normal form

4. Reduction to orbital normal form of a vector field on the plane

5. An Algorithm for Computing a New Normal Form for Dynamical Systems

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3. Unique Normal Form for a Class of Three-Dimensional Nilpotent Vector Fields;International Journal of Bifurcation and Chaos;2017-07

4. Normal forms for germs of vector fields with quadratic leading part. The remaining cases;Studia Mathematica;2017

5. The Complete Formal Normal Form for the Bogdanov-Takens Singularity;Moscow Mathematical Journal;2015