Magnetic oscillations of a fractional Hall dot

We show that a quantum dot in the fractional Hall regime exhibits mesoscopic oscillations in its thermodynamic properties with a period which is a multiple of the period for free electrons. Our calculations are performed for parabolic quantum dots with hard-core electron-electron interactions and are exact in the strong field limit for ${\mathit{k}}_{\mathit{B}}$T smaller than the fractional Hall gap. Explicit expressions are given for the temperature dependence of the amplitude of the oscillations.