  The space missions CoRoT and Kepler provide high quality data that allow us
to test the transport of angular momentum in stars by the seismic determination
of the internal rotation profile. Our aim is to test the validity of the
seismic diagnostics for red giants rotation that are based on a perturbative
method and to investigate the oscillation spectra when the validity does not
hold. We use a non-perturbative approach implemented in the ACOR code (Ouazzani
et al. 2012) that accounts for the effect of rotation on pulsations, and solves
the pulsation eigenproblem directly for dipolar oscillation modes. We find that
the limit of the perturbation to first order can be expressed in terms of the
rotational splitting compared to the frequency separation between consecutive
dipolar modes. Above this limit, non-perturbative computations are necessary
but only one term in the spectral expansion of modes is sufficient as long as
the core rotation rate remains significantly smaller than the pulsation
frequencies. Each family of modes with different azimuthal symmetry, m, has to
be considered separately. In particular, in case of rapid core rotation, the
density of the spectrum differs significantly from one m-family of modes to
another, so that the differences between the period spacings associated with
each m-family can constitute a promising guideline toward a proper seismic
diagnostic for rotation.

Solar and Stellar Astrophysics