  We develop non-Archimedean techniques to analyze the degeneration of a
sequence of rational maps of the complex projective line. We provide an
alternative to Luo's method which was based on ultra-limits of the hyperbolic
3-space. We build hybrid spaces using Berkovich theory which enable us to prove
the convergence of equilibrium measures, and to determine the asymptotics of
Lyapunov exponents.
