中科院数学与系统科学研究院
数学研究所
学术报告
动力系统研讨班
潘雯瑜（多伦多大学）
报告人：潘雯瑜（多伦多大学）
题 目：Exponential mixing of frame flows for geometrically finite hyperbolic manifolds with cusps
时 间：2022.12.08（星期四）09:00-10:00
地 点：腾讯会议：782 2460 5514
摘 要：I will present the joint work with Jialun Li and Pratyush Sarkar in the talk. As a final work to establish that the frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions are exponentially mixing with respect to the Bowen-Margulis-Sullivan measure: we focus on the case with cusps. To prove this, we utilize the countably infinite symbolic coding of the geodesic flow of Li-Pan and perform a frame flow version of Dolgopyat's method à la Sarkar-Winter and Tsujii-Zhang. This requires the local non-integrability condition and the non-concentration property but the challenge in the presence of cusps is that the latter holds only on a large proper subset. To overcome this, we use a large deviation property for symbolic recurrence to the large subset. It is proved by studying the combinatorics of cusp excursions and using an effective renewal theorem as in the work of Li; the latter uses the exponential decay of the transfer operators for the geodesic flow of Li-Pan.
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