Full paper in PDF:
$%M. Viana, Ergodic theory of interval exchange maps, Rev. Mat. Complut. 19 (2006), no. 1, 7100.%$

Ergodic Theory of Interval Exchange Maps
Marcelo VIANA
IMPA
Estrada Dona Castorina 110
22460 Rio de Janeiro Brazil

Received: November 10, 2005
Accepted: January 16, 2006
ABSTRACT

A unified introduction to the dynamics of interval exchange maps and related topics, such as the geometry of translation surfaces, renormalization operators, and Teichmüller flows, starting from the basic definitions and culminating with the proof that almost every interval exchange map is uniquely ergodic. Great emphasis is put on examples and geometric interpretations of the main ideas.

Key words: interval exchange map, translation surface, Abelian differential, Teichmüller flow.
2000 Mathematics Subject Classification:
37D25, 37D40, 37D50.