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math.GT2018
You can hear the shape of a billiard table: Symbolic dynamics and rigidity for flat surfaces
Moon Duchin, Viveka Erlandsson, Christopher J. Leininger +1
We give a complete characterization of the relationship between the shape of a Euclidean polygon and the symbolic dynamics of its billiard flow. We prove that the only pairs of tab…
math.GT2005★ 9 cited
Thin triangles and a multiplicative ergodic theorem for Teichmüller geometry
Moon Duchin
We show that, in the Teichmüller metric, "thin-framed triangles are thin"---that is, under suitable hypotheses, the variation of geodesics obeys a hyperbolic-like inequality. This…