  We compute the spectrum of the Feigenbaum period-doubling operator in the
space of bounded analytical functions in an ellipse. The spectral properties of
the period-doubling operator in this space are not the same as in the space of
even analytical functions. In particular, it was found that the dimension of
the unstable manifold is not one (Feigenbaum's conjecture), but three. We
analyze several articles devoted to this problem and compare different
approaches and algorithms.
