Dynamics on the infinite staircase | Zendy

W. Patrick Hooper | Zendy; Pascal Hubert | Zendy; Barak Weiss | Zendy

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Dynamics on the infinite staircase

Author(s) -

W. Patrick Hooper,

Pascal Hubert,

Barak Weiss

Publication year - 2013

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2013.33.4341

Subject(s) - ergodic theory , torus , lebesgue measure , surface (topology) , mathematics , lebesgue integration , cover (algebra) , measure (data warehouse) , lattice (music) , pure mathematics , mathematical analysis , radon , geometry , physics , computer science , quantum mechanics , acoustics , mechanical engineering , database , engineering

The paper is related to the satellite conference on “Various Aspects of Dynamical Systems,” following ICM 2010.International audienceFor 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

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