Hybrid dynamics of Hénon mappings

Abstract: For studying the meromorphic degeneration of complex dynamics, the theory of hybrid spaces, introduced by Boucksom, Favre and Jonsson, is known to be a strong tool. In this paper, we apply this theory to the dynamics of H\'enon maps. For a family of H\'enon maps ${H_t}_{t\in\mathbb{D}^*}$ that is parametrized by a unit punctured disk and meromorphically degenerates at the origin, we show that as $t\to 0$, the family of the invariant measures ${\mu_t}$ "weakly converges" to a measure on the Berkovich affine plane associated to the non-archimedean H\'enon map determined by the family ${H_t}_t$. We also calculate the limit of their Lyapunov exponents.