Comparison of dynamical degrees for semi-conjugate meromorphic maps

Let f X→ X be a dominant meromorphic map on a projective manifold X which preserves a meromorphic fibration π X→ Y of X over a projective manifold Y . We establish formulas relating the dynamical degrees of f , the dynamical degrees of f relative to the fibration and the dynamical degrees of the map g Y→ Y induced by f . Applications are given.