Dynamics on the infinite staircase

W. Patrick Hooper, Pascal Hubert, Barak Weiss

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)4341-4347
Number of pages7
JournalDiscrete and Continuous Dynamical Systems
Volume33
Issue number9
DOIs
StatePublished - 1 Sep 2013

Keywords

  • Dynamics
  • Ergodicity
  • Infinite lattice surface
  • Infinite staircase
  • Maharam measure

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