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

Degeneration of endomorphisms of the complex projective space in the hybrid space