阿诺索夫表征极限集的规律性

Pub Date : 2024-08-03 DOI:10.1112/topo.12355

Tengren Zhang, Andrew Zimmer

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引用次数: 0

摘要

在本文中，我们建立了对于某个 α ∈ ( 1 , 2 ) $alpha \ in (1,2)$ 的投影阿诺索夫表示的极限集是实投影空间的 C α $C^{\alpha }$ 子满面的必要条件和充分条件。我们还根据阿诺索夫表示的特征值数据计算了 α $\alpha$ 的最优值。

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Regularity of limit sets of Anosov representations

In this paper, we establish necessary and sufficient conditions for the limit set of a projective Anosov representation to be a $C^{α}$ -submanifold of the real projective space for some $α \in (1, 2)$ . We also calculate the optimal value of $α$ in terms of the eigenvalue data of the Anosov representation.

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