Projections of Polynomial Vector Fields and the Poincaré Sphere

AbstractWe investigate projections of homogeneous polynomial vector fields to level sets of homogeneous polynomials. This allows a systematic study of “stationary points at infinity” for polynomial differential equations inn-dimensional real space. Results include some general criteria for the existence of unbounded solutions, and a fairly complete discussion of boundedness of solutions for second-order equations in one dependent variabl