コロキウム

Codimension-two bifurcations are fundamental and interesting phenomena in dynamical systems, and fold-Hopf and double-Hopf bifurcations are the most important among them. We study the normal forms of these two codimension-two bifurcations, and obtain sufficient conditions for their nonintegrability in the meaning of Bogoyavlenskij. We reduce the problems to those of planar polynomial vector fields, and apply an approach recently proposed for such vector elds based on Ayoul and Zung's version of the Morales-Ramis theory. This is joint work with Primitivo Acosta-Humanez.