%0 Journal Article %T Dynamics on the infinite staircase %T Dynamique sur l'escalier infini %+ Department of Mathematics [Be'er Sheva] %+ Laboratoire d'Analyse, Topologie, Probabilités (LATP) %+ the City College of New York, Department of mathematics %A Weiss, Barak %A Hubert, Pascal %A Hooper, W. Patrick %Z The paper is related to the satellite conference on “Various Aspects of Dynamical Systems,” following ICM 2010. %< avec comité de lecture %@ 1078-0947 %J Discrete and Continuous Dynamical Systems - Series A %I American Institute of Mathematical Sciences %V 33 %N 9 %P 4341-4347 %8 2013-09 %D 2013 %R 10.3934/dcds.2013.33.4341 %K dynamics %K infinite staircase %K ergodicity %K Maharam measure %K infinite lattice surface %Z 37D50; 14H30, 30F30, 30F35, 37F30 %Z Mathematics [math]/Dynamical Systems [math.DS]Journal articles %X 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 ℤ-cover of the torus, reducing the question to the well-studied cylinder map. %G English %L hal-01299642 %U https://hal.science/hal-01299642 %~ CNRS %~ UNIV-AMU %~ EC-MARSEILLE %~ INSMI %~ TDS-MACS