By Martin Golubitsky
Bifurcation concept reports how the constitution of suggestions to equations adjustments as parameters are assorted. the character of those adjustments relies either at the variety of parameters and at the symmetries of the equations. quantity I discusses how singularity-theoretic suggestions reduction the certainty of transitions in multiparameter platforms. This quantity makes a speciality of bifurcation issues of symmetry and indicates how group-theoretic recommendations relief the knowledge of transitions in symmetric structures. 4 extensive issues are lined: staff idea and steady-state bifurcation, equicariant singularity thought, Hopf bifurcation with symmetry, and mode interactions. the hole bankruptcy presents an creation to those topics and motivates the learn of structures with symmetry. special case experiences illustrate how group-theoretic tools can be utilized to investigate particular difficulties coming up in applications.