Lyapunov exponents of Teichmüller flows
Teichmuller flow | Lyapunov exponent | asymptotic fla | asymptotic cycle
We study the dynamical properties of Teichmuller flows and renormalization operators in the moduli space of Abelian differentials, and use the conclusions to analyze the quantitative behavior of geodesics on typical translation surfaces. Three main results are reviewed: existence of asymptotic cycles, the asymptotic flag theorem, and simplicity of the Lyapunov spectrum. We give complete proofs of the first two and an outline for the last one.