Any smooth quasiperiodic potential with dihedral symmetry D_n (n≥3) and any number of quasiperiods has open level lines at a single energy value at most.
Dynnikov, Proof of S.P
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On the Novikov problem for dihedral symmetry potentials
Any smooth quasiperiodic potential with dihedral symmetry D_n (n≥3) and any number of quasiperiods has open level lines at a single energy value at most.