A note about the spectrum of composition operators induced by a rotation

[EN] A characterization of those points of the unit circle which belong to the spectrum of a composition operator C phi, defined by a rotation phi (z)=rz with |r|=1, on the space H0(D) of all analytic functions which vanish at 0, is given. Examples show that the spectrum of C phi need not be closed. In these examples the spectrum is dense but point 1 may or may not belong to it, and this is related to Diophantine approximation.