|
|
|
|
Литература
|
|
| |
| 1. |
L. Bowen, H. Li, “Harmonic models and spanning forests of residually finite groups”, J. Funct. Anal., 263:7 (2012), 1769–1808    |
| 2. |
R. Bowen, “Markov partitions for Axiom ${\rm A}$ diffeomorphisms”, Amer. J. Math., 92 (1970), 725–747 |
| 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 |
| 5. |
A. I. Danilenko, “Entropy theory from the orbital point of view”, Monatsh. Math., 134:2 (2001), 121–141 |
| 6. |
C. Deninger, “Fuglede–Kadison determinants and entropy for actions of discrete amenable groups”, J. Amer. Math. Soc., 19:3 (2006), 737–758 |
| 7. |
C. Deninger, “Determinants on von Neumann algebras, Mahler measures and Ljapunov exponents”, J. Reine Angew. Math., 651 (2011), 165–185 |
| 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 |
| 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 |
| 10. |
M. Einsiedler, K. Schmidt, “Markov partitions and homoclinic points of algebraic $\mathbb Z^d$-actions”, Динамические системы и смежные вопросы, Сборник статей. К 60-летию со дня рождения академика Дмитрия Викторовича Аносова, Труды МИАН, 216, Наука, М., 1997, 265–284  |
| 11. |
A. Furman, “Random walks on groups and random transformations”, Handbook of dynamical systems, v. 1A, North-Holland, Amsterdam, 2002, 931–1014 |
| 12. |
M. Göll, Principal algebraic actions of the discrete Heisenberg group, PhD Thesis, University of Leiden, 2015, 167 pp. |
| 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 |
| 14. |
B. Hayes, “Fuglede–Kadison determinants and sofic entropy”, Geom. Funct. Anal., 26:2 (2016), 520–606 |
| 15. |
R. Kenyon, A. Vershik, “Arithmetic construction of sofic partitions of hyperbolic toral automorphisms”, Ergodic Theory Dynam. Systems, 18:2 (1998), 357–372 |
| 16. |
D. Kerr, H. Li, Ergodic theory: Independence and Dichotomies, Springer Monographs in Mathematics, Springer, Cham, 2016 |
| 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 |
| 18. |
H. Li, “Compact group automorphisms, addition formulas and Fuglede–Kadison determinants”, Ann. of Math. (2), 176:1 (2012), 303–347 |
| 19. |
H. Li, A. Thom, “Entropy, determinants, and $L^2$-torsion”, J. Amer. Math. Soc., 27:1 (2014), 239–292 |
| 20. |
D. A. Lind, “Dynamical properties of quasihyperbolic toral automorphisms”, Ergodic Theory Dynam. Systems, 2:1 (1982), 49–68 |
| 21. |
D. Lind, K. Schmidt, “Homoclinic points of algebraic $Z^d$-actions”, J. Amer. Math. Soc., 12:4 (1999), 953–980 |
| 22. |
Д. Линд, К. Шмидт, “Обзор алгебраических действий дискретной группы Гейзенберга”, УМН, 70:4(424) (2015), 77–142 |
| 23. |
D. Lind, K. Schmidt, “New examples of Bernoulli algebraic actions”, Ergodic Theory Dynam. Systems, 42:9 (2022), 2923–2934 |
| 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 |
| 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 |
| 26. |
K. R. Parthasarathy, Probability measures on metric spaces, Probability and Mathematical Statistics, 3, Academic Press, Inc., New York–London, 1967 |
| 27. |
D. S. Passman, The algebraic structure of group rings, Pure Appl. Math., Wiley-Interscience [John Wiley & Sons], 1977 |
| 28. |
N. Sauer, “On the density of families of sets”, J. Combinatorial Theory Ser. A, 13 (1972), 145–147 |
| 29. |
K. Schmidt, Dynamical systems of algebraic origin, Progress in Mathematics, 128, Birkhäuser Verlag, Basel, 1995 |
| 30. |
K. Schmidt, “Representations of toral automorphisms”, Topology Appl., 205 (2016), 88–116 |
| 31. |
B. Seward, “Krieger's finite generator theorem for actions of countable groups I”, Invent. Math., 215:1 (2019), 265–310 |
| 32. |
B. Seward, “Krieger's finite generator theorem for actions of countable groups II”, J. Mod. Dyn., 15 (2019), 1–39 |
| 33. |
S. Shelah, “A combinatorial problem; stability and order for models and theories in infinitary languages”, Pacific J. Math., 41 (1972), 247–261 |
| 34. |
Я. Г. Синай, “Построение марковских разбиений”, Функц. анализ и его прил., 2:3 (1968), 70–80 |
| 35. |
N. Th. Varopoulos, “Long range estimates for Markov chains”, Bull. Sci. Math. (2), 109:3 (1985), 225–252 |
| 36. |
А. М. Вершик, “Арифметический изоморфизм гиперболических автоморфизмов тора и софических сдвигов”, Функц. анализ и его прил., 26:3 (1992), 22–27 |
| 37. |
B. Weiss, “Intrinsically ergodic systems”, Bull. Amer. Math. Soc., 76 (1970), 1266–1269 |
| 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 |
