Zeroes of complete polynomial vector fields

Bustinduy, Alvaro

doi:10.1090/S0002-9939-03-06943-0

Zeroes of complete polynomial vector fields
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by Alvaro Bustinduy PDF

Proc. Amer. Math. Soc. 131 (2003), 3767-3775 Request permission

Abstract:

We prove that a complete polynomial vector field on $\mathbb {C}^{2}$ has at most one zero, and analyze the possible cases of those with exactly one which is not of Poincaré-Dulac type. We also obtain the possible nonzero first jet singularities of the foliation $\mathcal {F}_X$ at infinity and the nongenericity of completeness. Connections with the Jacobian Conjecture are established.

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