Computational algebra for bifurcation theory
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. (c) 2005 Elsevier Ltd. All rights reserved.
standard bases local ring bifurcation point singularity theory