We consider tunneling through two point contacts between two edges of QuantumHall liquids of different filling factors $\nu_{0,1}=1/ (2m_{0,1}+1)$ with$m_0-m_1\equiv m>0$. Properties of the antidot formed between the pointcontacts in the strong-tunneling limit are shown to be very different from the$\nu_0 =\nu_1$ case, and include vanishing average total current in the twocontacts and quasiparticles of charge $e/m$. For $m>1$, quasiparticle tunnelingleads to non-trivial $m$-state dynamics of effective flux through the antidotwhich restores the regular ``electron'' periodicity of the current in fluxdespite the fractional charge and statistics of quasiparticles.
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