Algebraic invariant curves for the Liénard equation
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- by Henryk Żoła̧dek PDF
- Trans. Amer. Math. Soc. 350 (1998), 1681-1701 Request permission
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.References
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Additional Information
- Henryk Żoła̧dek
- Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
- Email: zoladek@mimuw.edu.pl
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 1681-1701
- MSC (1991): Primary 34C05, 58F21
- DOI: https://doi.org/10.1090/S0002-9947-98-02002-9
- MathSciNet review: 1433130