  We study degenerating families of hyperbolic dynamics over complex K3
surfaces by means of the theory of hybrid spaces by Boucksom, Favre, and
Jonsson. For an analytic family of hyperbolic automorphisms $\{f_t: X_t\to
X_t\}_{t\in\mathbb{D}^*}$ over K3 surfaces $X_t$ that is possibly
meromorphically degenerating at the origin, we consider the family of invariant
measures $\{\eta_t\}$ on $X_t$ constructed by Cantat. The family $f_t$ induces
a hyperbolic automorphism
$f_{\mathbb{C}((t))}^{\mathop{\mathrm{an}}}:X_{\mathbb{C}((t))}^{\mathop{\mathrm{an}}}\to
X_{\mathbb{C}((t))}^{\mathop{\mathrm{an}}}$ over the induced non-archimedean K3
surface, where we also have a measure $\eta_0$ by Filip. Our main theorem
states the weak convergence of $\{\eta_t\}$ to $\eta_0$ as $t\to0$ over the
induced so-called hybrid space.
