Geodesic
On a universal Borel adic space
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 24-38 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that the so-called uniadic graph and its adic automorphism are Borel universal, i.e., every aperiodic Borel automorphism is isomorphic to the restriction of this automorphism to a subset invariant under the adic transformation, the isomorphism being defined on a universal (with respect to the measure) set. We develop the concept of basic filtrations and combinatorial definiteness of automorphisms suggested in our previous paper. 
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A. M. Vershik; P. B. Zatitskii. On a universal Borel adic space. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 24-38. http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a2/

[1] A. M. Vershik, “Ravnomernaya algebraicheskaya approksimatsiya operatorov sdviga i umnozheniya”, DAN SSSR, 259:3 (1981), 526–529 | MR | Zbl

[2] A. M. Vershik, “Teorema o markovskoi periodicheskoi approksimatsii v ergodicheskoi teorii”, Zap. nauchn. sem. LOMI, 115, 1982, 72–82 | MR | Zbl

[3] A. M. Vershik, P. B. Zatitskii, “Universalnaya adicheskaya approksimatsiya, invariantnye mery i masshtabirovannaya entropiya”, Izv. RAN. Ser. matem., 81:4 (2017), 68–107 | DOI | MR | Zbl

[4] E. Glasner, B. Weiss, “On the interplay between measurable and topological dynamics”, Handbook of Dynamical Systems, v. 1B, eds. B. Hasselblatt, A. Katok, Elsevier, Amsterdam, 2006, 597–648 | MR | Zbl

[5] A. M. Vershik, “Teoriya filtratsii podalgebr, standartnost i nezavisimost”, Uspekhi mat. nauk, 72:2(434) (2017), 67–146 | DOI | MR | Zbl

[6] A. M. Vershik, P. B. Zatitskii, “Kombinatornye invarianty metricheskikh filtratsii i avtomorfizmov; universalnyi adicheskii graf”, Funkts. anal. i pril., 52:4 (2018), 23–37 | DOI

[7] A. Kechris, A. Louveau, “The classification of hypersmooth Borel equivalence relations”, J. Amer. Math. Soc., 10:1 (1997), 215–242 | DOI | MR | Zbl

[8] V. Kanovei, Borel Equivalence Relations. Structure and Classification, Amer. Math. Soc., Providence, RI, 2008 | MR | Zbl

[9] S. Thomas, “A descriptive view of unitary group representations”, J. European Math. Soc., 17 (2015), 1761–1787 | DOI | MR | Zbl

[10] K. Schmidt, “Unique ergodicity for quasi-invariant measures”, Math. Z., 167 (1979), 169–172 | DOI | MR | Zbl