Journal of Dynamical and Control Systems

, Volume 4, Issue 4, pp 539–581

Countable Set of Limit Cycles for the Equation \(\frac{{dw}}{{dz}} = \frac{{P_n \left( {z,w} \right)}}{{Q_n \left( {z,w} \right)}}\)

  • A.A. Shcherbakov
  • E. Rosales-González
  • L. Ortiz-Bobadilla


Differential equations on the complex plane with a rational right-hand side are considered. In a generic case such equation has a countable set of homologically independent limit cycles. It is proved that the exceptional set – the set of equations such that they do not have this property – has the real codimension at least two in the space of equations with right-hand side of degree no greater than a fixed number n.

Polynomial differential equations limit cycles monodromy group conformal maps fixed points 


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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • A.A. Shcherbakov
    • 1
  • E. Rosales-González
    • 2
  • L. Ortiz-Bobadilla
    • 2
  1. 1.Russian Academy of SciencesFrumkin Inst. of ElectrochemistryRussia
  2. 2.Instituto de Matemáticas, Universidad Nacional Autónoma de México, C.PMexico CityMéxico

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