Geodesic
Descriptive Kakutani equivalence
Journal of the European Mathematical Society, Tome 12 (2010) no. 1, pp. 179-219 Cet article a éte moissonné depuis la source EMS Press

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We consider a descriptive set-theoretic analog of Kakutani equivalence for Borel automorphisms of Polish spaces. Answering a question of Nadkarni, we show that up to this notion, there are exactly two aperiodic Borel automorphisms of uncountable Polish spaces. Using this, we classify all Borel R-flows up to C∞-time-change isomorphism. We then extend the notion of descriptive Kakutani equivalence to all (not necessarily injective) Borel functions, and provide a variety of results leading towards a complete classification. The main technical tools are a series of Glimm–Effros and Dougherty–Jackson–Kechris-style embedding theorems.
DOI : 10.4171/jems/194
Classification : 03-XX, 00-XX
Keywords: Borel functions, Borel ℝ-flows, Kakutani equivalence 
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     author = {Benjamin D. Miller and Christian Rosendal},
     title = {Descriptive {Kakutani} equivalence},
     journal = {Journal of the European Mathematical Society},
     pages = {179--219},
     year = {2010},
     volume = {12},
     number = {1},
     doi = {10.4171/jems/194},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/194/}
}
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Benjamin D. Miller; Christian Rosendal. Descriptive Kakutani equivalence. Journal of the European Mathematical Society, Tome 12 (2010) no. 1, pp. 179-219. doi: 10.4171/jems/194

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