Connecting orbits in highdimensional dynamical systems
50/96 Wolf-Jürgen Beyn, Thorsten Pampel (Göke).
A note on the Hopf stability formula under nonresonance
conditions
The Hopf stability formula determines
the super- or subcriticality of periodic branches at a Hopf
bifurcation point as well as the stability of the emanating
periodic orbits. The standard approach to this formula uses the
center manifold reduction and hence requires that there are no
further eigenvalues on the imaginary axis except for the
complex conjugate pair. In this paper we give a complete
derivation of this formula under the weaker nonresonance
condition which only excludes integer multiples of the purely
imaginary pair. We show that the shooting type approach in
[Amann 90] can be corrected in such a way that a full
algorithmic treatment of the stability formula becomes
possible.
