The general Li\'enard polynomial system

In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, we solve first the problem on the maximum number of limit cycles surrounding a unique singular point for an arbitrary polynomial system. Then, by means of the same bifurcationally geometric approach, we solve the limit cycle problem for a general Li\'enard polynomial system with an arbitrary (but finite) number of singular points. This is related to the solution of Hilbert's sixteenth problem on the maximum number and relative position of limit cycles for planar polynomial dynamical systems.