Theoretical framework demonstrates an upgrade method for mixing limit theorems in dynamical systems, suggesting new tools to evaluate closed geodesics on curved surfaces.
Motivated by work of Dolgopyat and N\'andori, we establish a general method for upgrading limit theorems for Birkhoff sums and cocycles over dynamical systems to mixing limit theorems under mild ergodicity and hyperbolicity assumptions. Building on previous work of Al-Saqban and Forni, we apply this method to obtain mixing limit theorems for particular subbundles of the Kontsevich-Zorich cocycle. In forthcoming work of Arana-Herrera and Honaryar these results are applied to study the arithmetic/homological complexity of long simple closed geodesics on negatively curved surfaces.
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Arana-Herrera et al. (2024) studied this question.
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