1:3 resonant double Hopf bifurcation

Abstract

This thesis was an attempt to study the behavior of the 1:3 resonant double Hopf bifurcation around the pure modes. This bifurcation is studied with a general 4D normal form, describing the evolution of two amplitudes and two phases. The pure modes are equilibiria which have one amplitude equal to zero. The thesis contains the derivation of the resonant normal form, the localization around a specific pure mode and an analysis of the resulting local system.

However due to a grave error made in the derivation of the normal form discovered in a very late stage of the writing, the thesis is incomplete. This means no interpretation and conclusion of the results are contained within this thesis. It does contain a incorrect and old version of the analysis to illustrate the consequences of the error.