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## Teaching

### UNIVERSITY OF CALIFORNIA, IRVINE

 2015-2016 1st term Math205A 2nd term Math205B Real Analysis 2nd term Math 3D Introduction to differential equations 2nd term Math117 Dynamical Systems 3rd term Math205C Real Analysis 2014-2015 1st term Math220A Analytic Functions Theory 2nd term Math220B Analytic Functions Theory 2nd term Math117 Dynamical Systems 3rd term Math220C Analytic Functions Theory 2013-2014 1st term Math211A Ergodic Theory 2nd term Math117 Dynamical Systems 3rd term Math141 Introduction to Topology 2012-2013 1st term Math220A Analytic Functions Theory 2nd term Math220B Analytic Functions Theory 2nd term Math2D Multivariable calculus 3rd term Math220C Analytic Functions Theory 2011-2012 1st term Math205A Real Analysis 2nd term Math205B Real Analysis 3rd term Math205C Real Analysis 2010-2011 1st term Math211A Dynamical Systems 1st term Math118A Theory of Differential Equations 2nd term Math211B Dynamical Systems 3rd term Math3D Introduction to differential equations 2009-2010 1st term Math220 A Analytic Functions Theory 2nd term Math220 B Analytic Functions Theory 3rd term Math 3D Introduction to differential equations 3rd term Math220 C Analytic Functions Theory 2008-2009 1st term Math 3D Introduction to differential equations 2nd term Math 140A Elementary Analysis 2007-2008 1st term Math120 A Introduction to Group Theory 2nd term Math220 B Analytic Functions Theory 3rd term Math211B Dynamical Systems

### CALTECH (2004-2007)

 2006-2007 1st term Ma147a Dynamical Systems 3rd term Ma 4 Introduction to Mathematical Chaos 3rd term Ma147b Hamiltonian Dynamics 2005-2006 1st term Ma108a Classical Analysis 2nd term Ma108b Classical Analysis 3rd term Ma 4 Introduction to Mathematical Chaos 2004-2005 1st term Ma 147a Dynamical Systems 2nd term Ma 108b Classical Analysis 3rd term Ma 147c Complex Dynamics

### MOSCOW STATE UNIVERSITY (2000-2003)

Ordinary Differential Equations
Introduction to Dynamical Systems
Differential Equations on Surfaces

### INDEPENDENT  UNIVERSITY OF MOSCOW (2000-2003)

Ordinary Differential Equations
Probability Theory
Dynamical Systems
Calculus

### BAUMAN MOSCOW STATE TECHNICAL UNIVERSITY (1996-1997)

Linear Algebra
Numerical Methods in Mathematics

## 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", to appear in Inventiones Mathematicae.

27. (with V.Kleptsyn) "Synchronization properties of random piecewise isometries", to appear in Communications in Mathematical Physics.

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", to appear in Contemporary Mathematics.

31. (with S.Northrup) "On Sums of Nearly Affine Cantor Sets", submitted.

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

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