To study of the meromorphic degeneration of dynamics,
the theory of hybrid spaces, established by Favre, is known to be a strong tool.
In this talk, we apply this theory to the dynamics of Hénon maps;
for a family of Hénon maps$\{H_t\}_t$ parametrized by a unit punctured disk
meromorphically degenerating at the origin, we show that as $t\to 0$,
the family of the invariant measures $\{\mu_t\}$ “weakly converges”
to the measure on the Berkovich affine plane
which is naturally defined by the family $\{H_t\}_t$,
in the sense of the theory of hybrid spaces.