Equilibrium and oscillations of a rotating star with a magnetic field

We consider a simplification of the relations used to represent non-linear forces as expansions over a complete system of orthogonal spherical vectors in analyses of the equilibrium of a rotating star with a magnetic field. S ince the equations describing stellar oscillations form an infinite system of coupled differential equations, the determination of the fundamental fre quencies in the low-frequency range and of the equilibrium magnetic structu res are quite complicated. In particular, the solution for an isolated magn etic flux tube is determined with account for the regularity condition for the field outside the tube. These calculations provide evidence that the tr ansverse sizes of such isolated flux tubes are small. We also discuss low-f requency oscillations in a local approximation in the case of rigid rotatio n of the medium. Equations describing the frequency splitting of g modes in a differentially rotating star are derived.