Publications

(joint with S. Favorov) A new description of uniformly spread discrete sets, preprint [ arXiv:math.MG/2510.11061 ]

(joint with T. Amrutam, Y. Jiang and A. Skalski) Invariant subalgebras rigidity for von Neumann algebras of groups arising as certain semidirect products, preprint [ arXiv:math.OA/2507.12824 ]

(joint with A.I. Danilenko) Irreducible Koopman representations for nonsingular actions on boundaries of rooted trees, preprint [ arXiv:math.DS/2503.03894 ]

(joint with S. Bezuglyi and O. Karpel) Measures and dynamics on Pascal-Bratteli diagrams, preprint [ arXiv:math.DS/2411.06280  ]

(joint with Y. Jiang) A character approach to the ISR property, preprint [ arXiv:math.OA/2410.14517 ]

(joint with D. Gaidashev) Wild attractors for Fibonacci maps, preprint [ arxiv:math.DS/2406.19019 ]

(joint with R. Grigorchuk) Characters and IRS's on branch groups and embeddings into hyperfinite factor, accepted for publication at Groups, Geometry and Dynamics [ arXiv:math.RT/2312.13124 ]

(joint with I. Gorbovickis and W. Tucker) Lower bounds on the Hausdorff dimension of some Julia sets, Nonlinearity, 36 (2023), 2867-2893; [ arXiv: math.DS/2204.07880 ] 

(joint with R. Grigorchuk) On spectral properties of the Schreier graphs of the Thompson group F, Trans. of AMS, 376 (2023), no. 4, 2787-2819.; [ arXiv: math.SP/2107.01109 ] 

On Lebesgue measure and Hausdorff dimension of Julia sets of real periodic points of renormalization, Bulletin Polish Acad. Sci. Math. 68 (2020), 151-168.

(joint with S. Sutherland) On the Lebesgue measure of the Feigenbaum Julia set, Invent. math. 221 (2020), 167-202; [ arXiv: math.DS/1712.08638 ]

(joint with M. Yampolsky) On computational complexity of Cremer Julia sets, Fund. Math. 252 (2021), no. 3, 343-353 [ arxiv: math.DS/1907.11047 ]

(joint with R. Grigorchuk) On the question "Can one hear the shape of a group?" and Hulanicki type theorem for graphs, Israel J. Math. 237 (2020), no. 1, 53-74; [ arXiv:math.GR/1809.04008 ]

(joint with K. Medynets) On invariant random subgroups of block-diagonal limits of symmetric groups, Proc. of AMS, 147 (2019), no. 6, 2481-2494; [ arXiv: math.GR / 1711.01653 ]

On irreducibility of Koopman representations corresponding to measure contracting actions, Groups, Geometry and Dynamics, 12 (2018), no. 4, 1417-1427; [ arxiv.math.RT/1512.02687 ]

(joint with M. Yampolsky) Almost every real quadratic polynomial has a poly-time computable Julia set, Found. Comp. Math., 18 (2018), no. 5, 1233-1243; [ arXiv: math.DS / 1702.05768 ]

(joint with R. Grigorchuk) On diagonal actions of branch groups and the corresponding characters,  J. Funct. Anal. 274 (2018), no. 11, 3033-3055; [ arxiv:math.RT/1412.5476 ]

(joint with R. Grigorchuk) On spectra of Koopman, groupoid and quasi-regular representations, Journal of Modern Dynamics, Volume 11 (2017), 99-123; [ arxiv:math.RT/1510.00897 ]

(joint with R. Grigorchuk) On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups, Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov,  AMS Cont. Math. Ser., Volume 692 (2017), 51-66; [ arxiv:math.RT/1508.05452 ].

(joint with M. Yampolsky) Poly-time Computability of the Feigenbaum Julia set, Ergodic Theory and Dynam. Sys., to appear. [ arXiv: math.DS/1404.1236 ]

(joint with D. Sauzin) On the resurgent approach to Ecalle-Voronin's invariants, Comptes Rendus Mathematique, Volume 353, 3 (2015), 265–271. [ arXiv: math.DS/1307.8095 ] 

(joint with D. Sauzin) The resurgent character of the Fatou coordinates of a simple parabolic germ, Comptes Rendus Mathematique, Volume 352, 3 (2014), 255-261. [ arXiv: math.DS/1307.8093 ]

Computability of the Julia set. Nonrecurrent critical orbits, Discrete and Continuous Dynamical Systems, Volume 34, 7 (2014), 2751-2778. [   arXiv: math.DS/1109.2946 ]

(joint with K. Medynets) Finite Factor Representations of Higman-Thompson groups, Groups, Geometry, and Dynamics 8 (2014). [ arXiv: math.RT/1212.1230 ]

(joint with K. Medynets) On Characters of Inductive Limits of Symmetric Groups, Journal of Functional Analysis 264 (2013), no.7, 1565-1598. [ arXiv: math.RT/1105.6325 ]

Characters on the Full Group of an Ergodic Hyperfinite Equivalence Relation, Journal of Functional Analysis 261 (2011), no. 6, 1401-1414. [ arXiv: math.RT/1005.4289 ]

(joint with S. Favorov), A uniformly spread measure criterion, Anal. Math. Phys., Volume 1, 2-3 (2011), 115-119. [ arXiv: math.CA/0805.0959 ]

(joint with T. Banakh and D. Repovs) Symmetric monochromatic subsets in colorings of the Lobachevsky plane, Discrete Math. Theor. Comput. Sci. 12 (2010), no. 1 12-20. [ arXiv: math.CO/0804.1335 ]

A description of characters on generalized groups of motions associated with GL(\infty,F_q), (Russian) Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki 2008, no. 10, 14-19.

(joint with N. Nessonov) Invariant states on the wreath product, preprint [ arXiv: math/RT/0903.4987 ]

(joint with N. Nessonov), Characters of projective representations of the infinite generalized symmetric group, (Russian) Mat. Sb. 199 (2008), no. 10, 3-32; translation in Sb. Math. 199 (2008), no. 9-10 , 1421-1450.

(joint with N. Nessonov), Projective characters of the infinite generalized symmetric group, (Russian) Funktsional. Anal. i Prilozhen. 42 (2008), no. 1, 82-85; translation in Funct. Anal. Appl. 42 (2008), no. 1, 69-71.

(joint with N. Nessonov), A description of characters on the infinite wreath product, Methods Funct. Anal. Topology 13 (2007), no. 4, 301-317. [ arXiv: math.RT/0510597 ]

Tame representations of the group GL(\infty,F_q) (Russian) Algebra i Analiz 18 (2006), no. 2, 57-79; translation in St. Petersburg Math. J. 18 (2007), no. 2, 223-239.