Curriculum vitae
Pedagogic activity
Principal results

List of publications

  1. Regular polygones in En, Vestnik MGU, ser. mat. mech., 1962, no 8, p. 18-24.
  2. Generation of limit cycles under the perturbation of the equation dw/dz=-Rz/Rw, where R(z,w) is a polynomial, Math. Sbornik, 1969, v.78, N 3, p.360-373.
  3. Example of equations dw/dz = P (z,w)/Q (z,w) having infinite number of limit cycles and arbitrary high Petrovskii-Landis genus, Math. Sbornik, 1969, v.80, N 3, p.388-404.
  4. Multivalued functions on commutative normed rings, Vestnik MGU, ser. mat., 1969, no. 5, p. 8-11.
  5. Nonalgebricity of the set of differential equations with the rational right hand side having multiple limit cycles, Math, Sbornik, 1970, v.83, N3, p.452-456.
  6. Distraction of cycles in the foliations to analytic curves, Math. Sbornik, 1972, v.67, N 1, p.58-66.
  7. Algebraic nonsolvability and almost algebraic solvability of the center-focus problem., Funct. Anal. Appl., 1972, v.6, N 3, p. 30-37.
  8. Foliations by analytic curves, Math. Sbornik, . 1972, v.88 N 4, p.558-577.
  9. On the problems of rectification and cycle formation, Math. Sbornik, 1973, vol.90, no.2, p.184-195.
  10. Nondegenerate B-groups, Docl. Acad. Nauk SSSR, tom 208 (1973), no 3, 207-209.
  11. (with Khovanskii) Galois theory for Fuchsian systems of differential equations with small coefficients, Preprint of the Institute of applied mathematics, no 117, 1974, Moscow.
  12. Analytic nonsolvability of the problem of Liapunov stability and topological classification for singular points of analytic systems of differential equations, Math. Sbornik, 1976, v.99, N.2, p.162-175.
  13. Some remarks on the topology of singular points of analytic differential equations in the complex domain and the theorem of Ladis, 1977, v.11, N 2, p.28-38.
  14. On zeros of special Abelian integrals in the real domain, Funct. Anal. and Pril. 1977, v.11, N 4, p.78-79.
  15. Multiplicity of limit cycles occurring under the perturbation of the Hamiltonian equations of the class P2/Q1 in the real and complex plane, Trudy sem. im. I.G.Petrovskogo, v.3, 1978, p. 29-40.
  16. The topology of phase portraits of analytic differential equations in the complex projective plane, Trudy sem. im. I.G.Petrovskogo, v.4, 1978, p.83-136 , English transl. Selecta Math. Sov., v.5, 1986, 141-199.
  17. Global and local aspects of the theory of complex diffe- rential equations. Proceedings of International Congress of Mathematicians. Helsinki, 1978, p.821-826.
  18. Divergence of the series that transform an analytic differential equation to the linear normal form at a singular point, Funct. Anal. and Pril. 1979, v.13, N 3, p.87-88.
  19. (with Piartli) Zero type neighborhoods of embedded complex tori, Trudy sem. im. I.G.Petrovskogo, 1979, v. 5, p.85-95.
  20. (with Piartli) Materialization of Poincare resonances and divergence of normalizing series, Trudy sem. im. I.G.Petrovskogo, 1981, v.7, p.3-49.
  21. In the normal forms theory under breaking of A.D.Brjuno conditions divergence is a rool and convergence is an exception, Vestnik MGU, ser. mat., 1981, no. 5, p. 10-16.
  22. (with Piartli) Materialization of Poincare resonances and divergence of normalizing series for polynomial differential equations, Trudy sem. im. I.G.Petrovskogo, 1982, v 8, p.111-127.
  23. (with Chetaev) On the dimension of attractors of some dissipative systems, Appl. Math. Mech., 1982, v.46, N 3, p.374-381.
  24. Positive type embeddings of elliptic curves to complex surfaces, Trudy MMO, 1982, v.46, p. 37-67.
  25. Weakly contracting systems and attractors of Galiorkin approximations of the Navier-Stokes equations on the two-torus, International Mech. Surveys, 1982, v.5, N 1, p.31-63, transl. in Selecta Math. Sov., v. 11 N 3, p. 203-239.
  26. Singular points and limit cycles of differential equations in the real and complex plane, Preprint NIVTS AN SSSR, Pushchino, 1982, 38 p.
  27. (with Piartli) A polynomial vector field with singular points of Poincaré type only, Funct. Anal. Appl., 1983, v.17, N.4, p.84-85.
  28. (with Elizarov) Remarks on orbital analytic classification of germs of vector fields, Math. Sbornik, 1983, v. 121, N 3 p.111-126.
  29. On the dimension of attractors of k-contracting evolutionary systems in infinite dimensional spaces, Vestnik MGU, ser. math., 1983, N 3, p. 52 - 59.
  30. Limit cycles of polynomial vector fields with nondegenerated singular points in the real plane, Funct. Anal. Appl., 1984, v.18, N.3, p.32-42.
  31. The finiteness problem for limit cycles of polynomial vector fields on the plane, germs of saddle resonant vector fields and nonHausdorff Riemann surfaces. In Lecture Notes in Math; 1060, 1984.
  32. Dulac's memoir "On limit cycles" and related topics of the theory of differential equations, Russian Math. Surveys, 1985, v.40, N.6, p.41-78.
  33. (with Arnold) Ordinary differential equations. In Encyclopedia of Mathematical Sciences, v 1, Moscow 1985, Springer 1986.
  34. (with Arnold, Afraimovich, Shil'nikov) Bifurcation theory. In Encyclopedia of Mathematical Sciences, v 5, Moscow 1986, Springer 1994.
  35. A criterion of steepness for analytic functions, Russian Math. Surveys, 1986, v.41, N.1, p.193-194.
  36. Separatrix bilaterals for planar vector fields, Vestnik MGU, ser. Math., 1986, N 4, p.25-31.
  37. Algebraically and analytically solvable local problems in theory of ordinary differential equations, Trudy sem. im. I.G.Petrovskogo, 1987, v 12, p. 118-136.
  38. Singular points of vector fields (sceintific commentary), in the book: I.G.Petrovskii, Selected papers, Moskow, Nauka, 1987, 373-402.
  39. Limit cycles in real and complex planes (sceintific commentary), in the book: I.G.Petrovskii, Selected papers, Moskow, Nauka, 1987, 402-418.
  40. (with Khovanskii) Galois groups, Stokes operators and Ramis theorem, Funct. Anal. and Appl., 1990, v.24, N 3, p.31-42.
  41. Finiteness theorems for limit cycles, Russian Math. Surveys, 1990, v.45, N 2, p.143-200.
  42. Stability of the equilibrium points in hamiltonian systems with two degrees of freedom. Publication de l'Institut de Recherche Mathematique Avancee, 1990, 437, 11p.
  43. Finiteness theorem for limit cycles. Proceedings of International Congress of Mathematicians, Kyoto, 1990, v.11, p.1259-1270.
  44. Finiteness theorems for limit cycles. Amer. Math. Soc., Transl. vol.94, 1991, 288 p. 45. Nonlinear Stokes Phenomena, in the book: Dynamical systems and related topics (Nagoya 1990), 155-165, World Sci. Publ, NJ, 1991.
  45. (with Yakovenko) Smooth normal forms for local families of diffeomorphisms and vector fields, Russian Math. Surveys, 1991, v.46, N 1, p.3-39.
  46. Relaxation fast linear oscillations, Russian Math. Surveys, 1991, v.46, N 2, p.217-218.
  47. The concept of minimal attractors and maximal attractors of partial differential equations of the Kuramoto-Sivashinski type. Chaos 1, 1991, N2, p.168-173.
  48. Global analysis of the phase portrait for the Kuramoto- Sivashinski equation. Journal of dynamics and Dif. Equations., 1992, vol.4, N 4, p. 585-615.
  49. Local dynamics and nonlocal bifurcations, in the book: Bifurcations and periodic orbits of vector fields (Montreal, PQ, 1992), 279-319, Kluwer, 1993.
  50. Editor of: Nonlinear Stokes Phenomena, series "Advances in Soviet Mathematics", v.14, Amer. Math. Soc., 1993, 287 p.
  51. Nonlinear Stokes Phenomena, p. 1-55, in the book [51].
  52. (with Elizarov, Shcherbakov, Voronin) Finitely generated groups of germs of one-dimensional conformal mappings, and invariants for complex singular points of analytic foliations of the complex plane, p. 57-106, in the book [51].
  53. (with Yakovenko) Nonlinear Stokes Phenomena in smooth classification problems, p.235-287, in the book [51].
  54. (with Yakovenko) Finite cyclicity of elementary polycycles. C.R.Acad.Sci., Paris, Serie 1, 316, 1993, p.1081-1086.
  55. Normal forms for local families and nonlocal bifurcations. Complex analytic methods in dynamical systems, Asterisque, 1994, 222, p.233-258.
  56. (with Piartly) Monodromy group at infinity of generic polynomial vector field in the complex projective plane, Russian Journal of Math. Physics v.2 n 3, 275 -315.
  57. Editor (with Yakovenko) of: Conerning Hilbert 16th problem, AMS, 1995, 219 pp.
  58. (with Yakovenko) Concerning Hilbert sixteenth problem, p. 1-20, in the book [58].
  59. (with Yakovenko) Finite cyclicity of elementary polycycles, in the book [58], pp. 21-96.
  60. (with Yakovenko ) Double exponential estimate for the number of real zeros of complete Abelian Integral, Invenciones Matematicae, 1995, 25, 673-695.
  61. (with Kotova) Smale's horseshoe. Mathematical footwear that left an imprint, Quantum, 1995, vol. 5, no 5, 13-18.
  62. (with Yakovenko ) Counting real zeros of function satisfying linear differential equations, Journal of Differential Equations, vol. 126. no 1, 1996, p. 87-105.
  63. (with Arkhipov A.) Jump of energy from low harmoniks to the high ones in the multidimensional Kuramoto-Sivashinski equation, Selecta Mathematica formerly Sovietica, 1994, 13, 183 -196.
  64. Limit cycles and nonlinear Stokes phenomena, p. 7-23, in the book: The Stokes phenomenon and Hilbert's 16th problem, World Scientific, 1996.
  65. Editor of: Differential equations with real and complex time, collection of papers, proceedings of the Steklov Instisute, v. 213, 1996.
  66. The nonlinear Riemann-Hilbert problem, in the book [66], pp. 6-29.
  67. (with Piartli) Rational differential equations with a nonfree monodromy group at infinity, in the book [66], pp. 50-67.
  68. (with Shcherbakov) On skew cylinders and simultaneous uniformization, in the book [66], p. 104-114.
  69. (with Gorodetski), Minimal and strange attractors, International Journal of Bifurcation and Chaos, 1996, v. 6, N 6, 1177-1183.
  70. Embedding theorems for local maps, slow-fast systems and bifurcations from Morse-Smale to Smale-Williams, in the book "Topics in singularities theory, V.I.Arnold's 60th anniversary collection", AMS Transl. ser 2, vol.180, 1997, p.127-149.
  71. (with Anosov, Aranson, Arnold, Bronstein, Grines) Ordinary differential equations and smooth dynamical systems, Springer, 1997, 233 p.
  72. (with Li Weigu), Nonlocal Bifurcations, a Monograph, published by AMS, ser. Mathematical surveys and Monographs, 1998, vol.66.
  73. Covering manifolds for analytic families of leaves of foliations by analitic curves, Topological Methods in Nonlinear Analysis, 1998, v.11, 361-373.
  74. (with Blinchevskaya) Estimate for the entropy dimension of the maximal attractor for k-contracting systems in an infinite-dimensional space, Russian Journal of Math. Physics, 1999, v.6, N1, pp.20-26.
  75. (with Kaloshin) Bifurcation of planar and spatial polycycles: Arnold's program and its development, in: Proccedings of the Arnoldfest, Fields Institute Communications v.24, 1999, 241-271.
  76. (with M. Saprykina) Embedding theorems for local families and oscilatory slow-fast systems, in: Progress in Nonlinear Science, v 1, Nizhny Novgorod, Russia, 2002, 389-410.
  77. (with Gorodetski) Some new robust properties of invariant sets and attractors of dynamical systems, Funct. Anal. Appl., 1999, v. 33, n 2, 16-32.
  78. (with Li Weigu), Nonlocal Bifurcations, a Monograph, Russian translation, edited, MCCME, Che-Ro, 1999.
  79. Hilbert type numbers for Abel equations, growth and zeroes of holomorphic functions, Nonlinearity, v. 13, 2000, 1337-1342.
  80. (with A. Gorodetski) Some properties of skew products over a horseshoe and solenoid, Procedings of the Steklov Institute, v 231, 2000, 96-118.
  81. (with F.Dumortier and C.Rousseau) Normal forms near a saddle-node and applications to finite cyclicity of graphics, ETDS, v 22, 2002, 783-818
  82. (with J.Guckenheimer) The duck and the devil: canards on the staircase, Moscow Mathematical Journal, v 1, no 1, 2001, 27-47
  83. (with A.Panov), Some upper estimates of the number of limit cycles of planar vector fields with applications to Lienard equation, Moscow Mathematical Journal, v 1, no 4, 2001, 583-599
  84. Centennial history of Hilbert's 16th problem, Bull AMS, v 39, no 3, 2002, 301-354
  85. (with V. Moldavskis) Morse-Smale diffeomorphisms of a circle and moduli of elliptic curves, Moscow Mathematical Journal, v 3, no 2, 2003, pp 1-10
  86. (with G. Buzzard and S, Hruska), Kupka-Smale theorem for polynomial automorphisms of \Bbb C2 and persistence of heteroclinic intersections, to appear
  87. Selected topics in differential equations with real and complex time, in book "Normal forms, bifurcations and finiteness problems in differential equations," Kluwer, to appear
  88. (with P. Hamke and S. Tabachnikov) Bringing Eastern European Mathematical Traditions to North American Students, Notices of the AMS, November 2003.