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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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


Authors: Kevin Hockett and Sita Ramamurti
Journal: Trans. Amer. Math. Soc. 345 (1994), 693-703
MSC: Primary 58F23; Secondary 30D20, 58F21
MathSciNet review: 1270665
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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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DOI: https://doi.org/10.1090/S0002-9947-1994-1270665-5
Article copyright: © Copyright 1994 American Mathematical Society