Determinacy of degenerate equilibria with linear part x'=y, y'= 0 using MACSYMA

摘要

A MACSYMA program is presented which implements Takens's method for proving determinacy of a flow in the neighborhood of an equilibrium point by successive blowup transformations. The program is applied to nonlinear systems with linear part x'= y, y'= 0, and an examination of the pattern of the results reveals an infinite sequence of determinacy theorems. The results are applied to the behavior of van der Pol's equation at infinity.