  We show that amplitude chimeras in ring networks of Stuart-Landau oscillators
with symmetry-breaking nonlocal coupling represent saddle-states in the
underlying phase space of the network. Chimera states are composed of
coexisting spatial domains of coherent and of incoherent oscillations. We
calculate the Floquet exponents and the corresponding eigenvectors in
dependence upon the coupling strength and range, and discuss the implications
for the phase space structure. The existence of at least one positive real part
of the Floquet exponents indicates an unstable manifold in phase space, which
explains the nature of these states as long-living transients. Additionally, we
find a Stuart-Landau network of minimum size $N=12$ exhibiting amplitude
chimeras
