Dynamical studyof the parameter space for the complexHenon family

尽管复Henon映射被认为是复维全纯动力系统中最标准的系统之一，但从拓扑和组合的角度对其Julia集的动力学研究还不是很成熟。我们为这种映射引入了一种称为Hubbard树的组合模型，并发展了一种称为迭代单元群的代数形式。此外，结合数值实验，我们还分析了Henon族参数空间中的动力学结构。

Although the complex Henon map is regarded as one of the most standard holomorphic dynamical systems in complex dimension two, the dynamical studyof its Julia set from the topological and combinatorial viewpoint has not been well developed. We introduced a combinatorial model called the Hubbard tree for such map and developed an algebraic formalism called the iterated monodromy group. Moreover, together with the help of numerical experiments, we also analyzed the dynamical structurein the parameter space of the Henon family.