Voir la notice de l'article provenant de la source Math-Net.Ru
@article{FAA_2024_58_1_a4, author = {Hanfeng Li and Klaus Schmidt}, title = {Intrinsic ergodicity, generators, and symbolic representations}, journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a}, pages = {50--83}, publisher = {mathdoc}, volume = {58}, number = {1}, year = {2024}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a4/} }
TY - JOUR AU - Hanfeng Li AU - Klaus Schmidt TI - Intrinsic ergodicity, generators, and symbolic representations JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 2024 SP - 50 EP - 83 VL - 58 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a4/ LA - ru ID - FAA_2024_58_1_a4 ER -
Hanfeng Li; Klaus Schmidt. Intrinsic ergodicity, generators, and symbolic representations. Funkcionalʹnyj analiz i ego priloženiâ, Tome 58 (2024) no. 1, pp. 50-83. http://geodesic.mathdoc.fr/item/FAA_2024_58_1_a4/
[1] L. Bowen, H. Li, “Harmonic models and spanning forests of residually finite groups”, J. Funct. Anal., 263:7 (2012), 1769–1808 | DOI | MR | Zbl
[2] R. Bowen, “Markov partitions for Axiom ${\rm A}$ diffeomorphisms”, Amer. J. Math., 92 (1970), 725–747 | DOI | MR | Zbl
[3] C.-S. Tullio, C. Miel, H. Li, Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity, 2021 http://math.buffalo.edu/~hfli/surjunctive-first.pdf
[4] N.-P. Chung, H. Li, “Homoclinic groups, IE groups, and expansive algebraic actions”, Invent. Math., 199:3 (2015), 805–858 | DOI | MR | Zbl
[5] A. I. Danilenko, “Entropy theory from the orbital point of view”, Monatsh. Math., 134:2 (2001), 121–141 | DOI | MR | Zbl
[6] C. Deninger, “Fuglede–Kadison determinants and entropy for actions of discrete amenable groups”, J. Amer. Math. Soc., 19:3 (2006), 737–758 | DOI | MR | Zbl
[7] C. Deninger, “Determinants on von Neumann algebras, Mahler measures and Ljapunov exponents”, J. Reine Angew. Math., 651 (2011), 165–185 | MR | Zbl
[8] C. Deninger, K. Schmidt, “Expansive algebraic actions of discrete residually finite amenable groups and their entropy”, Ergodic Theory Dynam. Systems, 27:3 (2007), 769–786 | DOI | MR | Zbl
[9] M. Einsiedler, H. Rindler, “Algebraic actions of the discrete Heisenberg group and other non-abelian groups”, Aequationes Math., 62:1–2 (2001), 117–135 | DOI | MR | Zbl
[10] M. Einsiedler, K. Schmidt, “Markov partitions and homoclinic points of algebraic $\mathbb Z^d$-actions”, Dinamicheskie sistemy i smezhnye voprosy, Sbornik statei. K 60-letiyu so dnya rozhdeniya akademika Dmitriya Viktorovicha Anosova, Trudy MIAN, 216, Nauka, M., 1997, 265–284 | MR
[11] A. Furman, “Random walks on groups and random transformations”, Handbook of dynamical systems, v. 1A, North-Holland, Amsterdam, 2002, 931–1014 | MR | Zbl
[12] M. Göll, Principal algebraic actions of the discrete Heisenberg group, PhD Thesis, University of Leiden, 2015, 167 pp. | Zbl
[13] M. Göll, K. Schmidt, E. Verbitskiy, “Algebraic actions of the discrete Heisenberg group: expansiveness and homoclinic points”, Indag. Math. (N.S.), 25:4 (2014), 713–744 | DOI | MR | Zbl
[14] B. Hayes, “Fuglede–Kadison determinants and sofic entropy”, Geom. Funct. Anal., 26:2 (2016), 520–606 | DOI | MR | Zbl
[15] R. Kenyon, A. Vershik, “Arithmetic construction of sofic partitions of hyperbolic toral automorphisms”, Ergodic Theory Dynam. Systems, 18:2 (1998), 357–372 | DOI | MR | Zbl
[16] D. Kerr, H. Li, Ergodic theory: Independence and Dichotomies, Springer Monographs in Mathematics, Springer, Cham, 2016 | DOI | MR | Zbl
[17] S. Le Borgne, “Un codage sofique des automorphismes hyperboliques du tore”, C. R. Acad. Sci. Paris Sér. I Math., 323:10 (1996), 1123–1128 | MR | Zbl
[18] H. Li, “Compact group automorphisms, addition formulas and Fuglede–Kadison determinants”, Ann. of Math. (2), 176:1 (2012), 303–347 | DOI | MR | Zbl
[19] H. Li, A. Thom, “Entropy, determinants, and $L^2$-torsion”, J. Amer. Math. Soc., 27:1 (2014), 239–292 | MR | Zbl
[20] D. A. Lind, “Dynamical properties of quasihyperbolic toral automorphisms”, Ergodic Theory Dynam. Systems, 2:1 (1982), 49–68 | DOI | MR | Zbl
[21] D. Lind, K. Schmidt, “Homoclinic points of algebraic $Z^d$-actions”, J. Amer. Math. Soc., 12:4 (1999), 953–980 | DOI | MR | Zbl
[22] D. Lind, K. Shmidt, “Obzor algebraicheskikh deistvii diskretnoi gruppy Geizenberga”, UMN, 70:4(424) (2015), 77–142 | DOI | MR | Zbl
[23] D. Lind, K. Schmidt, “New examples of Bernoulli algebraic actions”, Ergodic Theory Dynam. Systems, 42:9 (2022), 2923–2934 | DOI | MR | Zbl
[24] D. Lind, K. Schmidt, E. Verbitskiy, “Homoclinic points, atoral polynomials, and periodic points of algebraic $\mathbb{Z}^d$-actions”, Ergodic Theory Dynam. Systems, 33:4 (2013), 1060–1081 | DOI | MR | Zbl
[25] A. Pajor, Sous-espaces $l^n_1$ des espaces de Banach, With an Introduction by Gilles Pisier, Travaux en Cours, 16, Hermann, Paris, 1985 | MR
[26] K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, 3, Academic Press, Inc., New York–London, 1967 | MR
[27] D. S. Passman, The algebraic structure of group rings, Pure Appl. Math., Wiley-Interscience [John Wiley Sons], 1977 | MR | Zbl
[28] N. Sauer, “On the density of families of sets”, J. Combinatorial Theory Ser. A, 13 (1972), 145–147 | DOI | MR | Zbl
[29] K. Schmidt, Dynamical systems of algebraic origin, Progress in Mathematics, 128, Birkhäuser Verlag, Basel, 1995 | DOI | MR | Zbl
[30] K. Schmidt, “Representations of toral automorphisms”, Topology Appl., 205 (2016), 88–116 | DOI | MR | Zbl
[31] B. Seward, “Krieger's finite generator theorem for actions of countable groups I”, Invent. Math., 215:1 (2019), 265–310 | DOI | MR | Zbl
[32] B. Seward, “Krieger's finite generator theorem for actions of countable groups II”, J. Mod. Dyn., 15 (2019), 1–39 | MR | Zbl
[33] S. Shelah, “A combinatorial problem; stability and order for models and theories in infinitary languages”, Pacific J. Math., 41 (1972), 247–261 | DOI | MR | Zbl
[34] Ya. G. Sinai, “Postroenie markovskikh razbienii”, Funkts. analiz i ego pril., 2:3 (1968), 70–80 | MR | Zbl
[35] N. Th. Varopoulos, “Long range estimates for Markov chains”, Bull. Sci. Math. (2), 109:3 (1985), 225–252 | MR | Zbl
[36] A. M. Vershik, “Arifmeticheskii izomorfizm giperbolicheskikh avtomorfizmov tora i soficheskikh sdvigov”, Funkts. analiz i ego pril., 26:3 (1992), 22–27 | MR | Zbl
[37] B. Weiss, “Intrinsically ergodic systems”, Bull. Amer. Math. Soc., 76 (1970), 1266–1269 | DOI | MR | Zbl
[38] Sauer–Shelah lemma, Wikipedia, The Free Encyclopedia, accessed 21, October 2021
[39] W. Woess, Random walks on infinite graphs and groups, Cambridge Tracts in Mathematics, 138, Cambridge University Press, Cambridge, 2000 | MR | Zbl