Global Structure of Planar Quadratic Semi-Quasi-Homogeneous Polynomial Systems

Abstract

This paper study the planar quadratic semi-quasi-homogeneous polynomial systems (short for PQSQHPS). By using the nilpotent singular points theorem, blow-up technique, Poincaré index formula, and Poincaré compaction method, the global phase portraits of such systems in canonical forms are discussed. Furthermore, we show that all the global phase portraits of PQSQHPS can be classed into six topological equivalence classes.