The Abelian Hopf H mod K Theorem

We study the symmetries of periodic solutions from Hopf bifurcation in systems with finite abelian symmetries. Our main result, the Abelian Hopf H mod K Theorem, gives necessary and sufficient conditions for when H mod K periodic solutions can occur by Hopf bifurcation, as well as classifies their possible symmetries. The proof is instructive in that it constructs a -equivariant vector field that yields conjugate branches of Hopf-bifurcating, periodic solutions with specified spatio-temporal symmetries. We give examples of our results applied to the case when the symmetry group is Zl

• Type: Journal
• Year: 2010
• Where: SIAMADS
• Authors: Natasha Filipski, Martin Golubitsky
• Keywords: Hopf Bifurcation, Periodic Solutions, SIAMADS 2010, Symmetries