By Martin Golubitsky, Ian Stewart
Bifurcation conception reviews how the constitution of suggestions to equations adjustments as parameters are different. the character of those alterations relies either at the variety of parameters and at the symmetries of the equations. quantity I discusses how singularity-theoretic options relief the certainty of transitions in multiparameter structures. This quantity makes a speciality of bifurcation issues of symmetry and indicates how group-theoretic concepts relief the certainty of transitions in symmetric structures. 4 large issues are coated: crew idea and steady-state bifurcation, equicariant singularity thought, Hopf bifurcation with symmetry, and mode interactions. the hole bankruptcy presents an advent to those topics and motivates the examine of platforms with symmetry. specified case stories illustrate how group-theoretic tools can be utilized to investigate particular difficulties coming up in functions.
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