Publications

1. A. I. Danilenko and M. I. Vieprik, Rank-one nonsingular actions of countable groups and their odometer factors, Ergod. Theory & Dyn. Syst., 45(2025), 1078 — 1128.

2. A. I. Danilenko, Krieger's type for ergodic nonsingular Poisson actions of non-(T) locally compact groups, Ergod. Theory & Dyn. Syst., 43(2023), 2317–2353.

3. A. I. Danilenko and M. I. Vieprik, Explicit rank-one constructions for irrational rotations, Studia Math., 270(2023), 121–144.

4. A. I. Danilenko, Z. Kosloff and E. Roy, Nonsingular Poisson suspensions, J. d'Anal. Math., 146(2022), 741–790.

5. A. I. Danilenko, Haagerup property and Kazhdan pairs via ergodic infinite measure preserving actions, Studia Math., 265(2022), 211–226.

6. A. I. Danilenko and Z. Kosloff, Krieger's type of nonsingular Poisson suspensions and IDPFT systems, Proc. Amer. Math. Soc., 150(2022), 1541–1557.

7. A. I. Danilenko and M. Lemańczyk, Ergodic cocycles of IDPFT systems and nonsingular Gaussian actions, Ergod. Theory & Dyn. Syst., 42(2022), 1624–1654.

8. A. I. Danilenko, Z. Kosloff and E. Roy, Generic nonsingular Poisson suspension is of type III₁, Ergod. Theory & Dyn. Syst., 42(2022), 1415--1445.

9. A. I. Danilenko, On the bounded cohomology for ergodic nonsingular actions of amenable groups, Isr. J. Math., 243(2021), 421--436.

10. A. I. Danilenko, Rank-one actions, their (C,F)-models and constructions with bounded parameters, J. d'Anal. Math.,139(2019), 697--750.

11. A. I. Danilenko and M. Lemańczyk, K-property for Maharam extensions of nonsingular Bernoulli and Markov shifts, Ergod. Theory & Dyn. Syst., 39(2019), 3292--3321.

12. A. I. Danilenko, Weak mixing for nonsingular Bernoulli actions of countable amenable groups, Proc. Amer. Math. Soc., 147(2019), 4439--4450.

13. A. I. Danilenko, Infinite measure preserving transformations with Radon MSJ, Isr. J. Math., 228(2018), 21--51.

14. A. I. Danilenko, Directional recurrence and directional rigidity for infinite measure preserving actions of nilpotent lattices, Ergod. Theory & Dyn. Syst., 37(2017), 1841--1861.

15. A. I. Danilenko, Furstenberg entropy values for nonsingular actions of groups without property(T), Proc. Amer. Math. Soc., 145(2017), 1153--1161.

16. A. I. Danilenko, Mixing actions of zero entropy for countable amenable groups, Colloq. Math., 145(2016), 179--186.

17. A. I. Danilenko, Actions of finite rank: weak rational ergodicity and partial rigidity, Ergod. Theory & Dyn. Syst., 36(2016), 2138--2171.

18. A. I. Danilenko, Finite ergodic index and asymmetry for infinite measure preserving actions, Proc. Amer. Math. Soc.144 (2016), 2521--2532.

19. A. I. Danilenko and M. Lemańczyk, Odometer actions of the Heisenberg group, J. d'Anal. Math., 128(2016), 107--157.

20. A. I. Danilenko and A. V. Solomko, Simple mixing actions with uncountably many prime factors, Colloq. Math., 139(2015), 37--54.

21. A. I. Danilenko, Mixing actions of the Heisenberg group, Ergod. Th. & Dyn. Syst., 34(2014), 1142--1167.

22. A. I. Danilenko and M. Lemańczyk, Spectral multiplicities for ergodic flows, Discrete and Contin. Dynam. Systems - Series A, 33(2013), 4271--4289.

23. A. I. Danilenko, A survey on spectral multiplicities of ergodic actions, Ergod. Theory & Dyn. Syst., 33(2013), 81--117.

24. A. I. Danilenko, Flows with uncountable but meager group of self-similarities, Contemp. Math., Amer. Math. Soc., Providence, R.I., Vol. 567 (2012), 99--104.

25. A. I. Danilenko, New spectral multiplicities for mixing transformations, Ergod. Theory & Dyn. Syst., 32(2012), 517--534.

26. A. I. Danilenko and V. V. Ryzhikov, On self-similarities of ergodic flows, Proc. London Math. Soc.,104(2012), 431--454.

27. A. I. Danilenko and V. V. Ryzhikov, Mixing constructions with infinite invariant measure and spectral multiplicities, Ergod. Theory & Dyn. Syst., 31(2011), 853--873.

28. A. I. Danilenko and A. del Junco, Almost continuous orbit equivalence for non-singular homeomorphisms, Isr. J. Math., 183(2011), 165--188.

29. A. I. Danilenko and K. K. Park, Rank-one flows of transformations with infinite ergodic index, Proc. Amer. Math. Soc., 139(2011), 201--207.

30. A. I. Danilenko, Uncountable collection of mixing rank-one actions for locally normal groups, Semin. et Congr. de la SMF, 20(2011), 253--266.

31. A. I. Danilenko and A. V. Solomko, Ergodic Abelian actions with homogeneous spectrum, Contemp. Math., Amer. Math. Soc., Providence, R.I., Vol. 532 (2010),137--148.

32. A. I. Danilenko and V. V. Ryzhikov, Spectral multiplicities for infinite measure preserving transformations, Funct. Anal. Appl., 44(2010), 161-170.

33. A. I. Danilenko, On new spectral multiplicities for ergodic maps, Studia Math.,197(2010), 57--68.

34. A. I. Danilenko and A. H. Dooley, Simple Z²-actions twisted by aperiodic automorphisms, Isr. J. Math., 175(2010), 285--299.

35. A. I. Danilenko and D. J. Rudolph, Conditional entropy theory in infinite measure and a question of Krengel, Isr. J. Math., 172(2009), 93--117.

36. A. I. Danilenko and A. Solomko, Infinite measure preserving flows with infinite ergodic index, Colloq. Math., 115(2009), 13—19

37. A. I. Danilenko, Weakly mixing rank-one transformations conjugate to their squares, Studia Math., 187(2008), 75--93.

38. A. I. Danilenko and A. del Junco, Cut-and-stack simple weakly mixing map with countably many prime factors, Proc. Amer. Math. Soc., 136(2008), 2463--2472.

39. A. I. Danilenko, (C,F)-actions in ergodic theory, in ``Geometry and Dynamics of Groups and Spaces'', Progr. Math., 265(2008), Birkhauser Verlag, Basel, 325--351.

40. A. I. Danilenko and C. E. Silva, Mixing rank-one actions of locally compact Abelian groups, Ann. Inst. H. Poincare’, Probab. Statist., 43(2007), 375--398.

41. A. I. Danilenko, On simplicity concepts for ergodic actions, J. d'Anal. Math.,102(2007), 77--118.

42. A. I. Danilenko, Explicit solution of Rokhlin's problem on homogeneous spectrum and applications, Ergod. Th. & Dyn. Syst., 26(2006), 1467--1490.

43. A. I. Danilenko, Mixing rank-one actions for infinite sums of finite groups, Isr. J. Math., 156(2006), 341--358.

44. A. I. Danilenko and M. Lemańczyk, A class of multipliers for W^⊥, Isr. J. Math., 148(2005), 137--168.

45. A. I. Danilenko and C. E. Silva, Multiple and polynomial recurrence for abelian actions in infinite measure, J. London Math. Soc., 69(2004), 183--200.

46. A. I. Danilenko, Infinite rank one actions and nonsingular Chacon transformations, Illinois J. Math., 48(2004), 769—786

47. A. I. Danilenko and K. K. Park, Generators and Bernoullian factors for amenable actions and cocycles on their orbits, Ergod. Theory & Dyn. Syst. 22(2002), 1715--1745.

48. A. I. Danilenko, Strong orbit equivalence of locally compact Cantor minimal systems, Internat. J. Math. 12(2001), 113--123.

49. A. I. Danilenko, Funny rank-one weak mixing for nonsingular Abelian actions, Isr. J. Math.121(2001), 29--54.

50. A. I. Danilenko, Entropy theory from orbital point of view, Monatsh. Math., 134(2001), 121--141.

51. A. I. Danilenko and T. Hamachi, On measure theoretical analogues of the Takesaki structure theorem for type III factors, Colloq. Math., 84/85(2000), 485--493.

52. A. I. Danilenko, On subrelations of ergodic measured type III equivalence relations, Colloq. Math., 84/85(2000), 13--22.

53. A. I. Danilenko, On cocycles with values in group extensions. Generic results, Matemat. Fizika, Analiz, Geometriya, 7(2000),153--171.

54. A. I. Danilenko, Point realization of Boolean actions of countable inductive limits of locally compact groups, Matemat. Fizika, Analiz, Geometriya, 7(2000), 35-48.

55. A. I. Danilenko, Endomorphisms of measured equivalence relations, cocycles with values in non-locally compact groups and applications, Ergod. Theory & Dyn. Syst., 19(1999), 571--590.

56. A. I. Danilenko and M. Lemańczyk, Isometric extensions, 2-cocycles and ergodicity of skew products, Studia Math., 137(1999), 123--142.

57. A. I. Danilenko, Comparison of cocycles of measured equivalence relation and lifting problems, Ergod. Theory & Dyn. Syst., 18 (1998),125--151.

58. A. I. Danilenko, On non-coalescent ergodic skew products and semigroups of their commutors, Dop. Nats. Akad. Nauk Ukr., 1998, No 9, 17--21.

59. A. I. Danilenko, Quasinormal subrelations of ergodic equivalence relations, Proc. Amer. Math. Soc.,126 (1998), 3361--3370.

60. A. I. Danilenko, Garding domains for unitary representations of countable inductive limits of locally compact groups, Matemat. Fizika, Analiz, Geometriya, 3 (1996), 231--260.

61. A. I. Danilenko and V. Ya. Golodets, On extension of cocycles to normalizer elements, outer conjugacy and related problems, Trans. Amer. Math. Soc., 348 (1996), 4857--4882.

62. A. I. Danilenko, The topological structure of Polish groups and groupoids of measure space transformations, Publ. RIMS Kyoto Univ., 31 (1995), 913--940.

63. A. I. Danilenko, On cocycles compatible with normalizers of full groups of measure space transformations, Dop. Nats. Akad. Nauk Ukr., 1994, No 7, 14--17.

64. V. Ya. Golodets, A. I. Danilenko and S. I. Bezuglyi, On cocycles of ergodic dynamical systems and automorphisms compatible with them, Adv.in Soviet Math., 19 (1994), 73--96.

65. S. I. Bezuglyi, V. Ya. Golodets and A. I. Danilenko, On extension of 1-cocycles of dynamical systems on normalizer elements, Dokl. Akad. Nauk UkrSSR, Ser. A, 1989, 3--5 (in Russian).

66. V. Ya. Golodets and A. I. Danilenko, Ergodic actions of Abelian groups and properties of their joint actions, Teoriya Funksii, Funkts. Anal. i ikh Prilozh., 50(1988), 43--47 (in Russian), transl. in J.Soviet Math., 49 (1990), 1267--1269.

List of chapters in scientific monographs

1. A. I. Danilenko and C. E. Silva, Ergodic Theory: Nonsingular Transformations, in volume ``Ergodic Theory'' of Encyclopedia of Complexity and Systems Science; second edition Springer, 2023, 233--292.

2. A. I. Danilenko and C. E. Silva, Ergodic Theory: Nonsingular Transformations, in ``Encyclopedia of Complexity and Systems Science'', Springer, 2009, 3055--3083.

Editing books

Ergodic theory. Edited by Cesar E. Silva and Alexandre I. Danilenko, a volume in Encycl. Complex. Syst. Sci., Springer, New York, [2023], ©2023. xxi+694 pp., ISBN:978-1-0716-2387-9