Dynamical stability and Lyapunov exponents for holomorphic endomorphisms of P(k)

We introduce a notion of stability for equilibrium measures in holomorphic of endomorphisms of CP(k) and prove that it is equivalent to the of repelling cycles and equivalent to the existence of some holomorphic motion of Julia sets which we call equilibrium. We characterize the corresponding bifurcations by the strict of the sum of Lyapunov exponents or the instability of critical and analyze how repelling cycles may bifurcate. Our methods deeply the properties of Lyapunov exponents and are based on ergodic theory on pluripotential theory.