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Limit periodic sets in polynomial Liénard equations

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Organization
Abstract
In this paper we classify all limit periodic sets, as well bounded as unbounded ones, that occur in Liénard equations ẋ = y, ẏ = P(x) + yQ(x), with P and Q polynomials of respective degrees m and n with mn ≥ 1. We also classify the interior and exterior boundaries of the period annuli of such systems with special attention to the exterior boundary of the Hopf centers. We investigate under which conditions on (m, n) certain configurations can occur.
Keywords
Differential Equations

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Chicago
Luca, Stijn, and Freddy Dumortier. 2009. “Limit Periodic Sets in Polynomial Liénard Equations.” Qualitative Theory of Dynamical Systems 7 (2): 339–366.
APA
Luca, S., & Dumortier, F. (2009). Limit periodic sets in polynomial Liénard equations. QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 7(2), 339–366.
Vancouver
1.
Luca S, Dumortier F. Limit periodic sets in polynomial Liénard equations. QUALITATIVE THEORY OF DYNAMICAL SYSTEMS. 2009;7(2):339–66.
MLA
Luca, Stijn, and Freddy Dumortier. “Limit Periodic Sets in Polynomial Liénard Equations.” QUALITATIVE THEORY OF DYNAMICAL SYSTEMS 7.2 (2009): 339–366. Print.
@article{8581154,
  abstract     = {In this paper we classify all limit periodic sets, as well bounded as unbounded ones, that occur in Li{\'e}nard equations \.{x} = y, \.{y} = P(x) + yQ(x), with P and Q polynomials of respective degrees m and n with mn \ensuremath{\geq} 1. We also classify the interior and exterior boundaries of the period annuli of such systems with special attention to the exterior boundary of the Hopf centers. We investigate under which conditions on (m, n) certain configurations can occur.},
  author       = {Luca, Stijn and Dumortier, Freddy},
  issn         = {1575-5460},
  journal      = {QUALITATIVE THEORY OF DYNAMICAL SYSTEMS},
  language     = {eng},
  number       = {2},
  pages        = {339--366},
  title        = {Limit periodic sets in polynomial Li{\'e}nard equations},
  url          = {http://dx.doi.org/10.1007/s12346-008-0019-9},
  volume       = {7},
  year         = {2009},
}

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