Bounded polynomial vector fields

Anna Cima, Jaume Llibre
1990 Transactions of the American Mathematical Society  
We prove that, for generic bounded polynomial vector fields in R" with isolated critical points, the sum of the indices at all their critical points is (-1)" . We characterize the local phase portrait of the isolated critical points at infinity for any bounded polynomial vector field in R" . We apply this characterization to show that there are exactly seventeen different behaviours at infinity for bounded cubic polynomial vector fields in the plane.
doi:10.1090/s0002-9947-1990-0998352-5 fatcat:4nk7y6q5abhkpbtldcrvhl5hfi