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Title:
Ergodic properties of Billiards in Polygons, Renormalization and Hodge theory
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Abstract:
We survey old and new results on the ergodic theory of rational and non-rational billiards in polygons from the perspective of renormalization methods based on the so-called Teichmueller geodesic flow and related cocycles (Kontsevich--Zorich, twisted). We emphasize the role of Hodge theory in the analysis (just started in the case of the twisted cocycle) of their Lyapunov structure, which lies at the core of most of the results we will present.
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