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We introduce the notion of fractional bidromy which is the combination offractional monodromy and bidromy, two recent generalizations of Hamiltonianmonodromy. We consider the vibrational spectrum of the HOCl molecule which isused as an illustrative example to show the presence of nontrivial fractionalbidromy. To our knowledge, this is the first example of a molecular systemwhere such a generalized monodromy is exhibited.

Fractional bidromy in the vibrational spectrum of HOCl