The J-flow On Toric Manifolds

We study the J-flow on the toric manifolds, through study the transition map between the moment maps induced by two K"{a}hler metrics, which is a diffeomorphism between polytopes. This is similar to the work of Fang-Lai, under the assumption of Calabi symmetry, they study the monotone map between two intervals. We get a partial bound of the derivatives of transition map.