Recurrence in generic staircases

Serge Troubetzkoy

doi:10.3934/dcds.2012.32.1047

Article Contents

2012, Volume 32, Issue 3: 1047-1053. Doi: 10.3934/dcds.2012.32.1047

This issue Previous Article Multi-dimensional traveling fronts in bistable reaction-diffusion equations Next Article Veech groups, irrational billiards and stable abelian differentials

Recurrence in generic staircases

Serge Troubetzkoy^1,

1.
Aix-Marseille University, Centre de physique théorique, Fédération de Recherches des Unités de Mathématique de Marseille, and Institut de mathématiques de Luminy, Luminy, Case 907, F-13288 Marseille Cedex 9

Received: September 30, 2010

Revised: September 30, 2010

Published: February 2012

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Abstract

The straight-line flow on almost every staircase and on almost every square tiled staircase is recurrent. For almost every square tiled staircase the set of periodic orbits is dense in the phase space.

Keywords:

Recurrence,
translation surface.

Mathematics Subject Classification: Primary: 37D40, 37D50.

Citation:

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References

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