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Asymptotics of orbits of a Kolmogorov type planar vector field with a fixed Newton polygon


Author: F. Berezovskaya
Journal: Proc. Amer. Math. Soc. 142 (2014), 2671-2681
MSC (2010): Primary 34E05
Published electronically: May 9, 2014
MathSciNet review: 3209323
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Abstract: Using the Newton polygon technique we show that the orbits of a Kolmogorov type planar vector field, consisting of a finite sum of power terms, have power asymptotics while tending to the equilibria on the axes and on the boundary of the Poincaré sphere.


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Additional Information

F. Berezovskaya
Affiliation: Department of Mathematics, Howard University, Washington, DC 20059
Email: fberezovskaya@howard.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11972-1
Keywords: Planar vector field, Poincar\'e sphere, orbit asymptotics, Newton polygon
Received by editor(s): June 21, 2012
Received by editor(s) in revised form: August 5, 2012
Published electronically: May 9, 2014
Dedicated: Dedicated to the memory of Professor A. M. Molchanov
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.