Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Jiazhong Yang
Journal: Proc. Amer. Math. Soc. 131 (2003), 2715-2720.
MSC (2000): Primary 34K17, 37C15
Posted: 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 conjugated to each other provided their linear approximations have the same eigenvalues and the nonlinear parts are generic.

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