00973nas a2200109   4500008004300000245006600043210006600109520061200175100002200787700001800809856003600827       2007                        en_Ud  00aReciprocal transformations and flat metrics on Hurwitz spaces0 aReciprocal transformations and flat metrics on Hurwitz spaces3 aWe consider hydrodynamic systems which possess a local Hamiltonian structure of Dubrovin-Novikov type. To such a system there are also associated an infinite number of nonlocal Hamiltonian structures. We give necessary and sufficient conditions so that, after a nonlinear transformation of the independent variables, the reciprocal system still possesses a local Hamiltonian structure of Dubrovin-Novikov type. We show that, under our hypotheses, bi-hamiltonicity is preserved by the reciprocal transformation. Finally we apply such results to reciprocal systems of genus g Whitham-KdV modulation equations.1 aAbenda, Simonetta1 aGrava, Tamara  uhttp://hdl.handle.net/1963/2210