Computer algebra and bifurcations (Q1418826)

The authors investigate implicit linear and nonlinear differential equations using methods from computer algebra. They derive conditions under which these equations admit polynomial solutions. Moreover, the result is constructive, and the construction of the solution can be seen as quadratic Newton iteration. Finally, they apply their techniques to the equation \[ \dot y= -y^3+ ay+ b \] which is of relevance as a normal form of a simple bifurcation.