Dynamics near the essential singularity of a class of entire vector fields

Hockett, Kevin; Ramamurti, Sita

doi:10.1090/S0002-9947-1994-1270665-5

Dynamics near the essential singularity of a class of entire vector fields
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by Kevin Hockett and Sita Ramamurti PDF

Trans. Amer. Math. Soc. 345 (1994), 693-703 Request permission

Abstract:

We investigate the dynamics near the essential singularity at infinity for a class of zero-free entire vector fields of finite order, i.e., those of the form $f(z) = {e^{P(z)}}$ where $P(z) = {z^d}$ or $P(z) = a{z^2} + bz + c$. We show that the flow generated by such a vector field has a "bouquet of flowers" attached to the point at infinity.

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