WIAS Preprint No. 931, (2004)

On some classes of limit cycles of planar dynamical systems


  • Grin, Alexander
  • Schneider, Klaus R.

2010 Mathematics Subject Classification

  • 34C07 34C05 37C27


  • plane vector fields, maximal number of limit cycles, weakend Hilbert 16-th problem


We consider two-dimensional smooth vector fields $dx/dt = P(x,y), dy/dt = Q(x,y)$ and estimate the maximal number of limit cycles with special properties which are defined by means of generalized Dulac and Cherkas functions. In case that $P$ and $Q$ are polynomials we present results about the weakend 16-th problem of Hilbert.

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