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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Algebraic invariant curves for
the Liénard equation


Author: Henryk Zoladek
Journal: Trans. Amer. Math. Soc. 350 (1998), 1681-1701
MSC (1991): Primary 34C05, 58F21
MathSciNet review: 1433130
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Abstract: Odani has shown that if $\deg g\leq \deg f$ then after deleting some trivial cases the polynomial system $\dot {x}=y,\,\,\dot {y}=-f(x)y-g(x)$ does not have any algebraic invariant curve. Here we almost completely solve the problem of algebraic invariant curves and algebraic limit cycles of this system for all values of $\deg f$ and $\deg g$. We give also a simple presentation of Yablonsky's example of a quartic limit cycle in a quadratic system.


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Additional Information

Henryk Zoladek
Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
Email: zoladek@mimuw.edu.pl

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02002-9
PII: S 0002-9947(98)02002-9
Received by editor(s): April 10, 1995
Received by editor(s) in revised form: August 26, 1996
Additional Notes: Supported by Polish KBN Grant No 2 P03A 022 08
Article copyright: © Copyright 1998 American Mathematical Society