On Complexity of Problems of Power Geometry

Here we propose a classification of the complexity levels of problems of Power Geometry. The classification consists of 4 levels and is based on the complexity of the geometric objects corresponding to a problem in the space of power exponents. We give also a comparative survey of these objects and the based on their methods of analysis of solutions for systems of algebraic equations, for systems of ordinary differential equations and for systems of partial differential equations. We mention some publications where the methods of Power Geometry were effectively used.