  Tidally-excited inertial waves in stellar convective regions are a key
mechanism for tidal dissipation in stars and therefore the evolution of
close-in binary or planetary systems. As a first step, we explore here the
impact of latitudinal differential rotation on the properties of free inertial
modes and identify the different families of modes. We show that they differ
from the case of solid-body rotation. Using an analytical approach as well as
numerical calculations, we conclude that critical layers (where the
Doppler-shifted frequency vanishes) could play a very important role for tidal
dissipation.
