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Trajectories escaping to infinity in finite time


Author: J. K. Langley
Journal: Proc. Amer. Math. Soc. 145 (2017), 2107-2117
MSC (2010): Primary 30D30
DOI: https://doi.org/10.1090/proc/13377
Published electronically: January 11, 2017
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Abstract: If the function $ f$ is transcendental and meromorphic in the plane, and either $ f$ has finitely many poles or its inverse function has a logarithmic singularity over $ \infty $, then the equation $ \dot z = f(z)$ has infinitely many trajectories tending to infinity in finite increasing time.


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Additional Information

J. K. Langley
Affiliation: School of Mathematical Sciences, University of Nottingham, NG7 2RD, United Kingdom
Email: james.langley@nottingham.ac.uk

DOI: https://doi.org/10.1090/proc/13377
Received by editor(s): May 11, 2016
Received by editor(s) in revised form: July 4, 2016
Published electronically: January 11, 2017
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2017 American Mathematical Society