  We consider a meromorphic family of endomorphisms of degree at least 2 of a
complex projective space that is parameterized by the unit disk.We prove that
the measure of maximal entropy of these endomorphisms converges to the
equilibrium measure of the associated non-Archimedean dynamical system when the
system degenerates. The convergence holdsin the hybrid space constructed by
Berkovich and further studied by Boucksom and Jonsson. We also infer from our
analysis an estimate for the blow-up of the Lyapunov exponent near a pole in
one-dimensional families of endomorphisms.
