Hopf bifurcation in the presence of symmetry, center manifold and Liapunov-Schmidt reduction

P. Chossat and M. Golubitsky
Hopf bifurcation in the presence of symmetry, center manifold and Liapunov-Schmidt reduction
In: Oscillation, Bifurcation and Chaos. (F.V. Atkinson, W.F. Langford and A.B. Mingarelli, eds.) CMS-AMS Conf. Proc. Ser. 8 AMS, Providence, 1987, 343-352.

Abstract

Assume that the linear part of a vector field X is semisimple and has eigenvalues at +wi/-wi. We show that if the quadratic terms of X vanish when restricted to the center subspace, then to third order the Liapunov-Schmidt reduction for finding periodic solutions of X is already in Birkhoff normal form. Several examples of systems with symmetry that satisfy this hypothesis are discussed.

P. Chossat and M. Golubitsky Hopf bifurcation in the presence of symmetry, center manifold and Liapunov-Schmidt reduction In: Oscillation, Bifurcation and Chaos. (F.V. Atkinson, W.F. Langford and A.B. Mingarelli, eds.) CMS-AMS Conf. Proc. Ser. 8 AMS, Providence, 1987, 343-352.

Abstract

P. Chossat and M. Golubitsky
Hopf bifurcation in the presence of symmetry, center manifold and Liapunov-Schmidt reduction
In: Oscillation, Bifurcation and Chaos. (F.V. Atkinson, W.F. Langford and A.B. Mingarelli, eds.) CMS-AMS Conf. Proc. Ser. 8 AMS, Providence, 1987, 343-352.