Kerckhoff, S. P. Simplicial systems for interval exchange maps and measured foliations. (English) Zbl 0597.58024 Ergodic Theory Dyn. Syst. 5, 257-271 (1985). Summary: The spaces of interval exchange maps and measured foliations are considered and an alternative proof that almost all interval exchange maps and measured foliations are uniquely ergodic is given. These spaces are endowed with a refinement process, called a simplicial system, which is studied abstractly and is shown to be normal under a simple assumption. The results follow and thus are a corollary of a more general theorem in a broader setting. Cited in 30 Documents MSC: 37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) 28D99 Measure-theoretic ergodic theory Keywords:spaces of interval exchange maps; measured foliations PDF BibTeX XML Cite \textit{S. P. Kerckhoff}, Ergodic Theory Dyn. Syst. 5, 257--271 (1985; Zbl 0597.58024) Full Text: DOI References: [1] DOI: 10.1007/BF01214699 · Zbl 0308.28014 · doi:10.1007/BF01214699 [2] DOI: 10.1016/0040-9383(80)90029-4 · Zbl 0439.30012 · doi:10.1016/0040-9383(80)90029-4 [3] Keane, Israel J. Math. 26 pp 188– (1977) [4] DOI: 10.2307/1993640 · Zbl 0122.29804 · doi:10.2307/1993640 [5] DOI: 10.2307/1971341 · Zbl 0497.28012 · doi:10.2307/1971341 [6] Veech, Progress in Mathematics I pp 113– (1981) [7] Veech, J. Analyse Math. 33 pp 222– (1978) [8] Rees, Ergod. Th. & Dynam. Sys. 1 pp 461– (1981) [9] Rauzy, Acta Arith. 34 pp 315– (1979) [10] DOI: 10.2307/1971391 · Zbl 0486.28014 · doi:10.2307/1971391 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.