Applications of algebraic methods in solving the center-focus problem

Mihail Popa, Victor Pricop

The nonlinear differential system $\dot{x}={\sum }_{i=0}^{\ell }{P}_{m_i}(x,y),\dot{y}={\sum }_{i=0}^{\ell }{Q}_{m_i}(x,y)$ is considered, where $P_{m_i}$ and $Q_{m_i}$ are homogeneous poly…