Add to ORKGAsteroseismology provides information on the internal structure of stars by studying their pulsations. Among the targets of CoRot, Kepler or Tess satellites, there is an important part of rapidly rotating stars whose spectrum is still difficult to exploit. The poor understanding of the spectrum structure is one of the reasons for this difficulty. Asymptotic methods are effective to understand the organization of the spectrum and relate it to the physical properties of the star. Asymptotically, the propagation of acoustic rays is described by a Hamiltonian system. If the star is almost spherical, the dynamics of the system is completely integrable. However, the rotation flattens the star, resulting in a transition of the dynamics to a mixed ...
