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