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Dynamics on the infinite staircase

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  • For the 'infinite staircase' square tiled surface we classify the Radon invariant measures for the straight line flow, obtaining an analogue of the celebrated Veech dichotomy for an infinite genus lattice surface. The ergodic Radon measures arise from Lebesgue measure on a one parameter family of deformations of the surface. The staircase is a $\mathbb{Z}$-cover of the torus, reducing the question to the well-studied cylinder map.
    Mathematics Subject Classification: Primary: 37D50; Secondary: 14H30, 30F30, 30F35, 37F30.

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