论文标题
Hitchin表示的Lyapunov指数之间的差距
Gap between Lyapunov exponents for Hitchin representations
论文作者
论文摘要
我们研究Lyapunov指数，用于通过平行运输在测量流中定义的双曲线曲线上的扁平束指数。我们将它们视为Hitchin表示空间上的不变，并表明任何两个连续的Lyapunov指数之间都存在差距。此外，我们将Riemann表面的统一表示为具有极端间隙的表面。 证明的策略是将lyapunov指数与其他不变性的其他不变性相关联，其中差距结果已经可用，或者我们可以直接显示。特别是，首先，我们将lyapunov指数与与叶植物hölder同构相关的叶的lyapunov指数与riemann表面的单一切线束上的不稳定叶片相关的叶状lyapunov指数。其次，我们将它们与Bridgeman，Canary，Labourie和Sambarino开发的热力学形式主义的环境相关联。
We study Lyapunov exponents for flat bundles over hyperbolic curves defined via parallel transport over the geodesic flow. We consider them as invariants on the space of Hitchin representations and show that there is a gap between any two consecutive Lyapunov exponents. Moreover we characterize the uniformizing representation of the Riemann surface as the one with the extremal gaps. The strategy of the proof is to relate Lyapunov exponents in the case of Anosov representations to other invariants, where the gap result is already available or where we can directly show it. In particular, firstly we relate Lyapunov exponents to a foliated Lyapunov exponent associated to a foliation Hölder isomorphic to the unstable foliation on the unitary tangent bundle of a Riemann surface. Secondly, we relate them to the renormalized intersection product in the setting of the thermodynamic formalism developed by Bridgeman, Canary, Labourie and Sambarino.
