Selected publications

1. Iterated monodromy groups of quadratic polynomials, I, Groups, Geometry, and Dynamics, 2, (2008), No. 3, p. 309-336 (with Laurent Bartholdi).
2. A minimal Cantor set in the space of 3-generated groups, Geom. Dedicata, 124, (2007), No. 2, p. 153-190.
3. Self-Similar Groups, Operator Algebras and Schur Complement, Journal of Modern Dynamics, 1, (2007), No. 3, p. 323-370. (with Rostislav Grigorchuk), (preliminary version).
4. Self-similar groups and their geometry, São Paulo Journal of Mathematical Sciences, 1, (2007), No. 1, p. 41-96.
5. On classification of inductive limits of direct products of alternating groups, Journal of the London Mathematical Society, 75, (2007), No. 1, p. 146-162. (with Yaroslav Lavrenyuk).
6. Thurston equivalence of topological polynomials, Acta Math., 197, (2006), p. 1-51. (with Laurent Bartholdi), (preliminary version).
7. Self-similar groups, volume 117 of Mathematical Surveys and Monographs. Amer. Math. Soc., Providence, RI, 2005.
8. Self-similar inverse semigroups and Smale spaces, International Journal of Algebra and Computation, 16, no 5, (2006), p. 849-874.
9. Automata, groups, limit spaces, and tilings, J. Algebra, 305, (2006), no. 2, p. 629-663, (with André Henriques and Laurent Bartholdi), (preliminary version).
10. Amenable actions of nonabenable groups, Zapiski Nauchnyh Seminarov POMI, (2005), p. 85-95, and Journal of Mathematical Sciences, 140, (2006), no. 3, p. 391-397 (with Rostislav Grigorchuk).
11. Cuntz-Pimsner algebras of group actions, Journal of Operator Theory, 52, (2004), no. 2, p. 223-249. (preliminary version)
12. Dynamics of triangular transformations of sequences over finite alphabets, Math. Notes, 73, (2003), no. 3-4, p. 436-439 (with Eva Mochko and Vitaly Sushchanskii).
13. Post-critically finite self-similar groups, Algebra and Discrete Mathematics, 2, no 4, (2003) 21-32. (with Evgen Bondarenko)
14. Automorphisms of the binary tree: state-closed subgroups and dynamics of 1/2-endomorphisms, In T.W. Müller, editor, Groups: Topological, Combinatorial and Arithmetic Aspects, volume 311 of LMS Lecture Notes Series, pages 375-404, 2004. (with S.Sidki).
15. From fractal groups to fractal sets, In Peter Grabner and Wolfgang Woess, editors, Fractals in Graz 2001, Analysis-Dynamics-Geometry-Stochastics, volume 19 of Trends in Mathematics, Birkhäuser, (2003), pages 25-118 (with Laurent Bartholdi and Rostislav I. Grigorchuk). (see preliminary versions here and here).
16. Hyperbolic spaces from self-similar group actions, Algebra and Discrete Mathematics, 1, no 2, (2003), 68-77.
17. Virtual endomorphisms of groups, Algebra and Discrete Mathematics, 1, no 1, (2002), 96-136.
18. Rigidity of branch groups acting on rooted trees, Geom. Dedicata, 89, (2002), 159-179. (with Ya.Lavreniuk).
19. Conjugation in tree automorphism groups, Int. J. of Algebra and Computation, 11, (2001), no. 5, 529-547. (with P.W.Gawron and V.I.Sushchansky).
20. On confinal dynamics of rooted tree automorphisms, Computational and Geometric Aspects of Modern Algebra (Michael Atkinson et al., ed.), LMS Lecture Notes Series, volume 275, Cambridge Univ. Press, Cambridge, 2000, pp. 229-246. (with V.I.Sushchanky).
21. Stabilizers of transitive actions on locally finite graphs, International Journal of Algebra and Computation, 10, (2000), no. 5, 591-602.
22. The group of asynchronous automata and rational homeomorphisms of the Cantor set, Math. Notes, 67, (2000), no. 5, 577-581 (with R. Grigorchuk).
23. Automata, dynamical systems and groups, Proceedings of the Steklov Institute of Mathematics, 231, (2000), 128-203. (with R. I. Grigorchuk and V.I.Sushchansky).
24. Commensurators of groups and reversible automata, Dopov. Nats. Akad. Nauk Ukr., no 12, (2000), 36-39. (with Olga Macedonska and Vitali Sushchansky).
25. Uniformly bounded spaces, Voprosy Algebry, 14, (1999), 47-97.
26. Quasi-isometric hyperbolic groups are bi-Lipschitz equivalent, Dokl. Nat. Akad. Nauk Ukraine, (1998), no. 1, 32-35.
27. On equivalence of nets in hyperbolic spaces, Dokl. Nat. Akad. Nauk Ukraine, (1997), no. 11, 18-21.

Articles in Press

1. A group of non-uniform exponential growth locally isomorphic to IMG(z^2+i), to appear in Transactions of the AMS.
2. Symbolic dynamics and self-similar groups, to appear in "Holomorphic Dynamics and Renormalization, in Honour of John Milnor's 75th Birthday", volume 53 of Fields Communications Series.
3. C*-algebras and self-similar groups, to appear in Journal für die reine und angewandte Mathematik.
4. Combinatorics of polynomial iterations.
5. Groups and analysis on fractals, to appear in "Analysis on Graphs and its Applications", P. Exner, J. P. Keating, P. Kuchment, T. Sunada, and A. Teplyaev eds., vol. 77 of Proceedings of Symposia in Pure Mathematics, A.M.S. (with Alexander Teplyaev).

Preprints

1. Combinatorial models of expanding dynamical systems.
2. On amenability of automata groups. (with Laurent Bartholdi and Vadim Kaimanovich).
3. Free subgroups in groups acting on rooted trees.
4. An uncountable family of three-generated groups acting on the binary tree.