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.