ON THE ADELPHIC POTENTIALS COMPATIBLE WITH A SET OF PLANAR ORBITS

Given a planar potential B = B(x, y), compatible with a monoparametric family of planar orbits f(x, y) = c, we face the problem of producing potentials A = A(x, y), adelphic to B(x, y), i.e. nontrivial potentia ls which have in common with B(x, y) the given set of orbits. We estab lish a linear, second order partial differential equation for a functi on P(x, y) and we prove that, to any definite positive solution of thi s equation, there corresponds a potential A(x, y) adelphic to B(x, y).