The Cyclic Hopf H mod K Theorem

الأصل · EN

The H mod K theorem gives all possible periodic solutions in a Γ-equivariant dynamical system, based on the group-theoretical aspects. In addition, it classifies the spatio temporal symmetries that are possible. By the contrary, the equivariant Hopf theorem guarantees the existence of families of small-amplitude periodic solutions bifurcating from the origin for each C-axial subgroup of Γ¹. In this paper we identify which periodic solution types, whose existence is guaranteed by the H mod K theorem, are obtainable by Hopf bifurcation, when the group Γ is finite cyclic.