Resumen de Computational algebra for bifurcation theory

Karin Gatermann, Serkan Hosten

• We provide algorithmic methods for the solution of the classification problem of bifurcations by vanishing and non-vanishing derivatives. These methods come from a generalization of standard bases for modules in local rings. We introduce the necessary theory of bifurcations, provide the algorithmic tools, and show the effectiveness of these tools in several examples, including a new one.