## PUBLICATIONS AND PREPRINTS

1. "Hierarchy of attractors for Axiom A diffeomorphisms", Vestnik MSU, no.1 (1996), pp.84-86.

2. (with Yu. Ilyashenko) "Minimal and strange attractors", International Journal of Bifurcation and Chaos, vol.6, no.6 (1996), pp.1177-1183.

3. (with Yu. Ilyashenko) "Some new robust properties of invariant sets and attractors of dynamical systems", Functional Analysis and Applications, no.2, vol.33, 1999, pp.16-30.

4. (with Yu. Ilyashenko) "Some properties of skew products over the horseshoe and solenoid", Proc. of Steklov Institute, vol. 231 (2000), p. 96-118. (here in Russian)

5. (with Yu. Ilyashenko, V. Kleptsyn, M. Nalskij) "Non-removable zero Lyapunov exponent", Functional Analysis and Applications,vol 39 (2005), no.1, pp. 27-38. (here in Russian)

6. "Regularity of central leaves of partially hyperbolic sets and its applications", Izvestia RAN (The Newsletter of the Russian Academy of Science), vol.70 (2006), no.6, pp. 52-78. (here in Russian)

7. (with V. Kaloshin) "How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency", Advances in Mathematics, 208 (2007), pp. 710-797.

8. (with B. Hunt and V. Kaloshin) "Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systems", Vol. 2, Proceedings of ICM 2006, Madrid, Spain, European Math Society (2006) pp.27-55.

9.  (with L. Diaz) "Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes", Ergodic Theory and Dynamical Systems, vol. 29 (2009), no. 5, pp. 1479--1513.

10. (with V. Kaloshin) "Hausdorff dimension of oscillatory motions in the restricted planar circular three body problem and in Sitnikov problem", in preparation.

11. (with D.Damanik, M. Embree, and S.\ Tcheremchantsev) "The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian"Communications in Mathematical Physics, vol. 280 (2008), no. 2, pp. 499-516.

12. (with D.Damanik) "Hyperbolicity of the Trace Map for the Weakly Coupled Fibonacci Hamiltonian", Nonlinearity, vol. 22 (2009), pp. 123-143.

13. (with V.Kaloshin) "Conservative homoclinic bifurcations and some applications"Steklov Institute Proceedings, vol. 267 (dedicated to the 70th anniversary of Vladimir Arnold), pp. 76-90.

14. (with D.Damanik) "The Spectrum and the Spectral Type of the Off-Diagonal Fibonacci Operator", arXiv:0807.3024v2 [math.SP].

15. (with D.Damanik) "The Spectrum of the Weakly Coupled Fibonacci Hamiltonian"Electronic Research Announcements in Mathematical Sciences, vol. 16 (2009), pp. 23--29.

16. (with Ch.Bonatti and L.Diaz) "Non-hyperbolic ergodic measures with large support"Nonlinearity, vol. 23 (2010), no. 3, pp. 687--705.

17. (with D.Damanik) "Spectral and Quantum Dynamical Properties of the Weakly Coupled Fibonacci Hamiltonian",  Communications in Mathematical Physics, vol. 305 (2011), pp. 221--277.

18. "On stochastic sea of the standard map"Communications in Mathematical Physics, vol. 309 (2012), no. 1, pp. 155–192.

19. (with D.Damanik) "The Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian"Geometric and Functional Analysis (GAFA), vol. 22 (2012), pp. 976--989.

20. (with D.Damanik) "Holder Continuity of the Integrated Density of States for the Fibonacci Hamiltonian", Communications in Mathematical Physics, vol.323 (2013), pp. 497-515.

21. (with D.Damanik and M.Embree) "Spectral Properties of Schrodinger Operators Arising in the Study of Quasicrystals", chapter in the book "Mathematics of Aperiodic Order" (editors Johannes Kellendonk, Daniel Lenz, Jean Savinien), series "Progress in Mathematics" (Birkhaeuser), vol.309 (2015).

22. (with D.Damanik and J.Fillman) "Continuum Schrodinger Operators Associated With Aperiodic Subshifts"Annales Henri Poincare, vol. 15 (2014), no. 6, pp. 1123--1144.

23. (with D.Damanik and B.Solomyak) "Absolutely Continuous Convolutions of Singular Measures and an Application to the Square Fibonacci Hamiltonian"Duke Mathematical Journal, 164 (2015), pp. 1603--1640.

24. (with T.Golenishcheva-Kutuzova, V.Kleptsyn and D.Volk) "Translation numbers define generators of $F_k^+\to {\text{\rm Homeo}_+}(\mathbb{S}^1)$"Moscow Mathematical Journal, vol. 14 (2014), no. 2, pp. 291--308.

25. (with D.Damanik) "Almost Ballistic Transport for the Weakly Coupled Fibonacci Hamiltonian"Israel Journal of Mathematics, vol. 206 (2015), 109-126

26. (with D.Damanik and W.Yessen) "The Fibonacci Hamiltonian"Inventiones Mathematicae, vol. 206 (2016), pp. 629--692.

27. (with V.Kleptsyn) "Synchronization properties of random piecewise isometries"Communications in Mathematical Physics, vol. 345 (2016), pp. 781--796.

28. (with D.Damanik) "Almost Sure Frequency Independence of the Dimension of the Spectrum of Sturmian Hamiltonians",  Communications in Mathematical Physics, vol. 337 (2015), pp. 1241--1253.

29. (with D.Damanik, Q.H.Liu, and Y.H.Qu)  "Transport Exponents of Sturmian Hamiltonians"Journal of Functional Analysis, vol. 269 (2015), pp.1404--1440.

30. (with Ya.Pesin) "Path connectedness and entropy density of the space of hyperbolic ergodic measures", Contemporary Mathematics, vol. 692 (2017), pp. 111--121.

31. (with S.Northrup) "On Sums of Nearly Affine Cantor Sets"Fundamenta Mathematicae, vol. 240 (2018), pp. 205--219.

32. (with D.Damanik) "An Extension of the Kunz-Souillard Approach to Localization in One Dimension and Applications to Almost-Periodic Schrödinger Operators",  Advances in Mathematics, vol. 297 (2016), pp. 149--173.

33. (with D.Damanik) "Sums of regular Cantor sets of large dimension and the Square Fibonacci Hamiltonian", permanent preprint.

34. (with D.Damanik) "Spectral transitions for the square Fibonacci Hamiltonian", Journal of Spectral Theory, vol. 8 (2018), pp. 1487–1507.

35. (with V.Kleptsyn) "Parametric Furstenberg Theorem on Random Products of SL(2,R) matrices", Advances in Mathematics, vol. 378 (2021), 107522.

36. (with J.Fillman and D.Damanik) "Multidimensional Almost-Periodic Schrödinger Operators with Cantor Spectrum", Annales Henri Poincare, vol. 20 (2019), pp. 1393–1402.

37. (with J.Fillman and D.Damanik) "Multidimensional Schrödinger Operators Whose Spectrum Features a Half-Line and a Cantor Set", Journal of Functional Analysis, vol. 280 (2021), 108911.

38. (with D.Damanik) "Must the Spectrum of a Random Schrodinger Operator Contain an Interval?", to appear in CMP.