  Oscillations have been detected in a variety of stars, including
intermediate- and high-mass main sequence stars. While many of these stars are
rapidly and differentially rotating, the effects of rotation on oscillation
modes are poorly known. In this communication we present a first study on
axisymmetric gravito-inertial modes in the radiative zone of a differentially
rotating star. These modes probe the deep layers of the star around its
convective core. We consider a simplified model where the radiative zone of a
star is a linearly stratified rotating fluid within a spherical shell, with
differential rotation due to baroclinic effects. We solve the eigenvalue
problem with high-resolution spectral simulations and determine the propagation
domain of the waves through the theory of characteristics. We explore the
propagation properties of two kinds of modes: those that can propagate in the
entire shell and those that are restricted to a subdomain. Some of the modes
that we find concentrate kinetic energy around short-period shear layers known
as attractors. We characterise these attractors by the dependence of their
Lyapunov exponent with the \BV frequency of the background and the oscillation
frequency of the mode. Finally, we note that, as modes associated with
short-period attractors form dissipative structures, they could play an
important role for tidal interactions but should be dismissed in the
interpretation of observed oscillation frequencies.
