Hopf bifurcation withSN-symmetry

摘要: We study Hopf bifurcation with SN-symmetry for the standard absolutely irreducible action of SN obtained from by permutation N coordinates. Stewart (1996 Symmetry methods in collisionless many-body problems, J. Nonlinear Sci. 6 543–63) obtains a classification theorem C-axial subgroups × S1. use this to prove existence branches periodic solutions symmetry systems ordinary differential equations posed on direct sum two such SN-absolutely representations, as result occurring real parameter is varied. determine (generic) conditions coefficients fifth order S1-equivariant vector field that describe stability and criticality those solution branches. finish paper an application cases = 4 5.