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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Differentiable conjugacy of the Poincaré type vector fields on $\mathbf{R}^3$


Author: Jiazhong Yang
Journal: Proc. Amer. Math. Soc. 131 (2003), 2715-2720
MSC (2000): Primary 34K17, 37C15
Published electronically: April 23, 2003
MathSciNet review: 1974327
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Abstract: We prove that on ${\mathbf R}^3$, except for those germs of vector fields whose linear parts are conjugated to $\lambda x\partial/\partial x +\lambda y \partial/\partial y +2\lambda z \partial/\partial z$, any two Poincaré type vector fields are at least $C^3$ conjugated to each other provided their linear approximations have the same eigenvalues and the nonlinear parts are generic.


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Additional Information

Jiazhong Yang
Affiliation: MAM, Institute of Mathematics, Peking University, Beijing, 100871, People’s Republic of China
Email: yang@sxx0.math.pku.edu.cn, jyang@math.pku.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07140-5
PII: S 0002-9939(03)07140-5
Keywords: Conjugacy, Poincar\'e type vector fields, moduli, normal form, resonance
Received by editor(s): August 20, 2000
Published electronically: April 23, 2003
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2003 American Mathematical Society