@article{cc37b778a73141ab9a4d2aac3f5d116b,
title = "Exchange transformations reversing orientation",
abstract = "Exchange transformations have emerged as an essential object of study in the theory of dynamical systems and ergodic theory. These theories arise in studying flat metrics, measurable foliations, and polygonal billiards. It is observed that any exchange transformation has an invariant Lebesgue measure, coinciding with the standard measure on the interval or the circle. Several aspects associated with the existence of ergodic interval exchange transformations, with flips on the interval are also explained. The definition of an exchange transformation needs to be modified in the presence of flips, to ensure its single-value at the discontinuity points.",
author = "C. Gutierrez and S. Lloyd and B. Pires and Zhuzhoma, {E. V.} and Medvedev, {V. S.}",
note = "Funding Information: C. Gutierrez acknowledges the support of FAPESP (grant no. 03/03107-9), CNPq (grant no. 470957/2006-9), and Brazil (grant no. 306328/2006-2). S. Lloyd acknowl- edges the support of FAPESP, grant no. 06/52650-5. B. Pires acknowledges the support of FAPESP, grant no. 06/60600-8 (Brazil). E. V. Zhuzhoma and V. S. Med-vedev acknowledge the support of the Russian Foundation for Basic Research, project nos. 08-01-00547a and 05-01-00501. Funding Information: This work began during E. V. Zhuzhoma{\textquoteright}s visit to Institute of Mathematical and Computer Sciences, University of S{\~a}o Paulo (Brazil) in March of 2007. E. V. Zhuzhoma thanks C. Gutierrez for hospitality and the University of S{\~a}o Paulo for financial support of the visit.",
year = "2008",
month = aug,
doi = "10.1134/S106456240804008X",
language = "English",
volume = "78",
pages = "500--502",
journal = "Doklady Mathematics",
issn = "1064-5624",
number = "1",
}