Under uniform hyperbolicity of minimal configurations, twist maps exhibit a complete devil's staircase for rotation numbers versus cohomology classes; the staircase is incomplete when positive-measure KAM tori exist.
Generic properties and problems of minimizing measures of Lagrangian systems.Nonlinearity, 9(2):273–310, 1996
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On Aubry's completeness conjecture
Under uniform hyperbolicity of minimal configurations, twist maps exhibit a complete devil's staircase for rotation numbers versus cohomology classes; the staircase is incomplete when positive-measure KAM tori exist.