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.
@article{urn:eudml:doc:40876,
title = {Ergodic theory of interval exchange maps.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {19},
year = {2006},
pages = {7-100},
zbl = {1112.37003},
mrnumber = {MR2219821},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40876}
}
Viana, Marcelo. Ergodic theory of interval exchange maps.. Revista Matemática de la Universidad Complutense de Madrid, Tome 19 (2006) pp. 7-100. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40876/