Preprint A461/2006
Ergodic theory of interval exchange maps
Marcelo Viana
Keywords: Interval exchange map | teichmuller flow | translation surface
A unified introduction to the dynamics of interval exchange maps and related topics, such as the geometry of translation surfaces, renormalization operators, and Teichmuller 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.