论文标题
部分可观测时空混沌系统的无模型预测
Entropy rigidity for cusped Hitchin representations
论文作者
论文摘要
我们为所有几何有限的紫红色基团的Hitchin表示建立了一个熵定理，该组概括了Potrie和Sambarino定理，用于封闭表面基团的Hitchin表示。在此过程中，我们介绍了（1,1,2） - 干横向组的类别，并为一个小组展示其锥形极限集的Hausdorff尺寸与其（第一个）简单的根部熵一致，为Kleinian群体和Pozzetti，Sambarino和Wienhard和Anosososs而言，为Bishop and Jones的结果提供了普遍的概括。我们还介绍了投影可见群体的横向表示理论，作为研究线性群体的离散亚组的工具，而线性群的离散亚组不一定是Anosov或相对呈Anosov。
We establish an entropy rigidity theorem for Hitchin representations of all geometrically finite Fuchsian groups which generalizes a theorem of Potrie and Sambarino for Hitchin representations of closed surface groups. In the process, we introduce the class of (1,1,2)-hypertransverse groups and show for such a group that the Hausdorff dimension of its conical limit set agrees with its (first) simple root entropy, providing a common generalization of results of Bishop and Jones, for Kleinian groups, and Pozzetti, Sambarino and Wienhard, for Anosov groups. We also introduce the theory of transverse representations of projectively visible groups as a tool for studying discrete subgroups of linear groups which are not necessarily Anosov or relatively Anosov.
