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Jet rigidity of Mather's $β$-function and complexified KAM curves holomorphic in potential for analytic standard maps
Mather's $β$-function associates with each rotation number the least average action carried by an orbit of a twist map. For analytic standard maps in the KAM regime, we prove the following. For any family of $d \ge 1$ directions of perturbation satisfying a natural symmetry condition, the jet of the
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