论文标题
Hénon映射的混合动力学
Hybrid dynamics of Hénon mappings
论文作者
论文摘要
为了研究复杂动力学的混合性变性，Boucksom，Favre和Jonsson引入的杂化空间理论是强大的工具。在本文中，我们将该理论应用于Hénon地图的动力学。对于一个hénon的家庭地图$ \ {h_t \} _ { Berkovich仿射平面与由家庭确定的非架构Hénon地图关联的$ \ {h_t \} _ t $。我们还计算其Lyapunov指数的极限。
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 Hénon maps. For a family of Hénon 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 $\{μ_t\}$ "weakly converges" to a measure on the Berkovich affine plane associated to the non-archimedean Hénon map determined by the family $\{H_t\}_t$. We also calculate the limit of their Lyapunov exponents.
