  We analyze Hamiltonian equivalence between Jordan and Einstein frames
considering a mini-superspace model of flat Friedmann-Lemaitre-Robertson-Walker
(FLRW) Universe in Brans-Dicke theory. Hamiltonian equations of motion are
derived in the Jordan, Einstein, and in the anti-gravity (or anti-Newtonian)
frames. We show that applying the Weyl (conformal) transformations to the
equations of motion in the Einstein frame we did not get the equations of
motion in the Jordan frame. Vice-versa, we re-obtain the equations of motion in
the Jordan frame applying the anti-gravity inverse transformation to the
equation of motion in the anti-gravity frame.

General Relativity and Quantum Cosmology;Cosmology and Nongalactic Astrophysics;High Energy Physics - Theory