Research papers and preprints in chronological order

 

 1. `` How projections affect the dimension spectrum of fractal measures”, with B. Hunt, Nonlinearity, 10, (1997), no. 5, 1031—1046,  [PDF];

 2. ``Some prevalent properties of smooth dynamical systems”, Proceedings of the Steklov Institute of Mathematics, 213, (1997), 123—151;

3. ``Prevalence in spaces of smooth mappings and a prevalent Kupka-Smale theorem” (in Russian), Dokl. Akad. Nauk, 355, (1997), no. 3, 306—307;

4. ``Prevalence in spaces of finitely smooth mappings”, Functional Analysis and its Application, 31, (1997), no. 2, 95—99;

5. ``Bifurcations of planar and spatial polycycles: Arnold's program and its development”, with Yu.S.Ilyashenko, Fields Institute Communications, 24, (1999), 241—271, [PDF];

6. ``Regularity of of embeddings of infinite-dimensional fractal sets into finite-dimensional spaces”, with B. Hunt, Nonlinearity, Vol. 12, (1999), no. 5, 1263—1275, [PDF];

7. ``An extension of Artin-Mazur theorem”, Annals of Mathematics, vol. 150, no. 2 (1999), 429—441, [PDF];

8. ``Generic diffeomorphisms with superexponential growth of number of periodic points”, Comm. in Math. Physics, Vol. 211, (2000), 1, 253—271, [PDF];

9. ``Nonsymmetric random walks along orbits of ergodic automorphisms”, with Ya.G.Sinai, Amer. Math. Soc. Transl.(2), 198, (2000), 109—115, [PDF];

10. ``Simple random walks along orbits of Anosov diffeomorphisms”, with Ya.G.Sinai,   Proc. of Steklov Math. Inst., 228, (2000), 224—233, [PDF];  

11. ``Diophantine Properties of Elements of SO(3)”, with I.Rodnianski, Geom. and Func. Anal, 11, (2001), 953—970, [PDF];

12. ``Hilbert-Arnold Problem and an estimate for cyclicity of polycycles on the plane and     in the space”,  Func Anal and its Appl, 35, no. 2, (2001), 146—147, [PDF];

13. ``A stretched exponential bound on the rate of growth of the number of periodic points   for prevalent diffeomorphisms”, I & II. Electron. Res. Announc. Amer. Math. Soc. 7 (2001), 17—27 [PDF]; & 28—36, [PDF];

14. ``A stretched exponential bound on the rate of growth of the number of periodic points  for prevalent diffeomorphisms II”, preprint, 2002, 85pp, [PDF];

15. ``Hausdorff Dimension of Linear Escape points for periodic Stochastic Dispersions”,  with D. Dolgopyat and L. Koralov, J. Stat. Physics, Vol 108, (2002), 943—971, [PDF];

16. ``The Existential Hilbert Problem  and  an estimate on cyclicity of elementary polycycles”, Inventiones Mathematica, 151 (2003), no. 3, 451—512, [PDF];

17. ``Geometric proofs of Mather's accelerating and connecting theorems”, Topics in Dynamics and Ergodic Theory (eds. S. Bezuglyi and S. Kolyada), London Mathematical Society, Lecture Notes Series, Cambridge University Press, 2003, 81—106, [PDF]; 

18.  ``Instability of  totally elliptic points  of  symplectic maps in dimension 4”,   Instability of resonant totally elliptic points of symplectic maps in dimension 4, with J. Mather and E. Valdinoci,  Analyse complexe, systèmes dynamiques, sommabilité des séries divergentes et théories galoisiennes. II. Asterisque, no. 297, (2004), 79—116,  [PDF];

19. `` Sample Path Properties of Stochastic Flows”, with D. Dolgopyat and L. Koralov, Annals of Probability, Vol. 32, no. 1A, (2004), 1—27, [PDF];

20. ``A Limit Shape Theorem for Stochastic Dispersions”,  with D. Dolgopyat and L. Koralov, Comm. in Pure and Appl. Math., Vol. 57, no. 9, (2004), 1127—1158, [PDF];

21. ``Growth of the number of periodic points”,   in Normal forms, Bifurcations and Finiteness Problems in Differential Equations (eds. Y. Ilyashenko and C. Rousseau),    Kluwer 2004, 355—385, [PDF];

22. ``Long time behaviour of periodic stochastic disperions”, with D. Dolgopyat and L. Koralov, XIVth International Congress on Mathematical Physics,  290—295,        World Sci. Publ., Hackensack, NJ, 2005, [PDF];

23. ``A Geometric Proof of Existence of Whitney Stratifications”, Moscow Math. Journ.,  Vol. 5 (2005), no.1, 125—133, [PDF];

24. `` Around Hilbert-Arnold Problem”,  in ``On finiteness in differential equations and Diophantine geometry”, 111—162, CRM Monogr. Ser., 24, Amer. Math. Soc.,       Providence, RI, 2005,  [PDF];

25. ``Mather theory, weak KAM, and viscosity solutions of Hamilton—Jacobi  PDE's”,  EQUADIFF 2003, 39—48, World Sci. Publ., Hackensack, NJ, 2005, [PDF];

26. ``Diffusion for Hamiltonian perturbations of integrable systems in high dimensions”,  with J. Bourgain, Journ. of Func. Analysis, 229,  (2005), no 1, 1—61, [PDF];

27. `` Remote Periodic and Quasiperiodic Motions  in  the  Planar  Circular  Restricted          3-Body Problem of KAM and Aubry-Mather Type”, with T. Nguyen, preprint, 2005, 35pp, [PDF];

28. ``The effect of projections on fractal sets and measures in Banach spaces”, with B.Hunt and W.Ott, Ergodic Theory and Dynamical Systems, 26, no. 3, (2006), 869—891, [PDF];

29. ``Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical system”,  with B. Hunt and V. Kaloshin, Vol. 2,   Proceedings of ICM 2006, Madrid, Spain, European Math Society (2006), 27—55, [PDF];

30. ``A stretched exponential bound on the rate of growth of the number of periodic points  for prevalent diffeomorphisms I”, with B. Hunt, Annals of Mathematics, 165 (2007), 89—170, [PDF];

31. ``How often surface diffeomorphisms have infinitely many sinks and hyperbolicity of periodic points near a homoclinic tangency”,   with A. Gorodetski,  Advances in Mathematics, 208 (2007), 710—797, [PDF];

32. ``An example of Arnold diffusion for nearly integrable Hamiltonian systems”,   with Mark Levi, Bulletin of AMS, Vol. 45, no. 3, July 2008, 409—427, [PDF];

33.``Geometry of Arnold diffusion”, with Mark Levi,  SIAM Review, Vol. 50,  no. 4,  2008, 702—720, [PDF];

34. ``Conservative homoclinic bifurcations and some applications”, with Anton Gorodetski,  Steklov Institute Proceedings, Vol. 267 (2009), dedicated to the 70th anniversary of   Vladimir Arnold, [PDF];

35. ``Almost dense orbit on energy surface”, with Ke Zhang and Yong Zheng, Proceedings  of XVITH International Congress on Mathematical Physics.  Held 3-8 August 2009 in Prague, Czech Republic. Edited    by Pavel Exner (Doppler Institute, Prague, Czech Republic). Published by World Scientific Publishing Co, 314—322, [PDF];

36. ``Prevalence”, with B. Hunt , chapter 2, Handbook in dynamical systems, edited by H. Broer, F. Takens, B. Hasselblatt, Vol. 3,  (2010),  43—87, [PDF]; see also http://www.sciencedirect.com/science/article/pii/S1874575X10003103

37. ``A C^r unimodal map with an arbitrary fast growth of the number of periodic points”, with O. Kozlovsky, preprint, (2002), 7pp, Ergodic Th. & Dynam. Systems, 2011, [PDF];

38. ``Destruction of invariant curves in the restricted planar circular three body problem  using action comparison”, with J. Galante, Duke Math J, Vol. 159, no. 2, (2011), 275—327, [PDF];

39. `` Finiteness of central configurations of five bodies in the plane”, with A. Albouy, 54pp,  Annals of Mathematics, (2012), [PDF];

40. ``Arnold diffusion in a pendulum lattice”, with M. Levi and M. Saprykina, preprint,  2010, 22pp,  submitted, [PDF];

41. ``An example of a nearly integrable Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension”, with M. Saprykina, preprint, 2010, 51pp, to appear in CMP, [PDF];

42. `` The method of spreading cumulative twist and application to the restricted planar circular three body problem”, with J. Galante, preprint, 2010, 48pp, [PDF];

43. ``Destruction of invariant curves in the restricted planar circular three body problem  using ordering condition”, with J. Galante, preprint, 2010, 28pp, [PDF];

44. `` Arnold diffusion in arbitrary degrees of freedom and 3-dimensional normally hyperbolic invariant cylinders”, with P. Bernard and K. Zhang, preprint, 2011, 70pp, [PDF];

45. ``Diffusion along mean motion resonance for the restricted planar three body problem”, with J. Fejoz, M. Guardia, P. Roldan, preprint, 2011, 68pp, submitted, [PDF];

46. ``Hausdorff dimension of oscillatory motions for restricted three body problems”, with  A. Gorodetski, preprint, 2011, 70pp, [PDF];

47. `` Normally normally hyperbolic invariant manifolds near strong double resonance’’, with K. Zhang, preprint, 2011, 44pp, [PDF];

48. `` Growth of Sobolev norms in the cubic defocusing nonlinear Schodinger equation’’, with M. Guardia, preprint,  73pp, 2012, [PDF];

49. `` On conjugacy of convex billiards’’, with A. Sorrentino, preprint,  23pp, 2012, [PDF];