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Юлий Сергеевич Ильяшенко,

доктор физико-математических наук, профессор, ректор Независимого Московского Университета

[Photo]

Curriculum vitae

Graduated Mechanical Mathematical Department of Moscow State University, 1968.

PhD in Mechanical Mathematical Department of Moscow State University, 1969, ``GENERATION OF LIMIT CYCLES UNDER PERTURBATIONS OF DIFFERENTIAL EQUATIONS $dw/dz = -R_z(z,w)/R_w(z,w)$, WHERE $R$ IS A POLYNOMIAL''.

From May 1968 Assistant Professor, from June 1972 Associated Professor, from August 96 Professor of Mechanical Mathematical Department of Moscow State University, Rector of the Independent University of Moscow, from November 1994.

Leading Scientist of Steklov Math. Institute of Russia Acad. of Sciences, half position, from June 95,

Professor of the Department of Mathematics of the Cornell University (half time position for the fall semesters, 1997 - 2001)

Member of the Bureau of Moscow Mathematical Society, from September 1993.

Vice-President of the Moscow Mathematical Society, from September 1996.

Member of the Editorial boards of the journals:

Doctoral thesis "TOPOLOGY OF PHASE PORTRAITS OF DIFFERENTIAL EQUATIONS IN THE REAL AND COMPLEX PLANES", Steklov Institute, November 1994. \newline \newline

Pedagogic activity

Courses for graduate students:

The courses were mostly given several times and permanently modified.

For undergraduate students:

PhD theses made under advisorship of Yu. Ilyashenko

Participation in international congresses and conferences

One or two-hour addresses in the conferences

Courses in international workshops and schools

Principal scientific achievements

  1. Proof of the Dulac's conjecture: Polynomial vector field in the real plane has but a finite number of limit cycles. The proof of this short statement requires a book [33] published by AMS in 1991; it was the subject of the talk in the ICM-1990. This proof was obtained in the competition with the French team: Ecalle, Martinet, Moussu, Ramis. The proof of the same conjecture given by Ecalle and based on the ideas of the four authors appeared in a book published in 1992. Preliminary studies: [22], [24], [27], [30].
  2. Investigation of generic properties of polynomial vector fields in the complex plane (talk in the ICM-1978) [12], [13], [44].
  3. Solvability of local problems of ODE:
  4. Geometric theorems on divergence of normalizing series and related topics in complex analysis [14],[15],[16],[19].
  5. Upper estimate of the Hausdorff and box counting dimensions for attractors of dissipative systems, with applications to Navier-Stokes and Kuramoto-Sivashinsky equations: [17], [18] (prolonged by Babin-Vishik),[21], [34], [37], [47].
  6. Nonlinear Stokes Phenomena: advisorship of the investigations of Voronin, Elizarov, Shcherbakov, summarized in [38], including [39], [40], [41].
  7. Generation of limit cycles under perturbation of planar Hamiltonian systems. Related study of zeroes of Abelian integrals by means of the theory of Riemann surfaces and other tools of complex analysis (like Riemann--Roch and Picard--Lefshetz theorems). Initiated in [1], [2], prolonged [3], [10], [45], [46].
  8. Normal forms for local families and nonlocal bifurcations. A complete list of finitely smooth integrable normal forms for local families of vector fields and maps [35], [41]. Solution of the Hilbert--Arnold problem for elementary polycycles [42], [49] (together with Yakovenko). Systematic exposition of the nonlocal bifurcations theory in the multidimensional space (together with Li Weigu) [54]. The book [54] containes new proofs of classical theorems and many new results.

Principal references

  1. Generation of limit cycles under the perturbation of the equation $dw/dz=-R_z/R_w$, where $R(z,w)$ is a polynomial, Math. Sbornik, 1969, v.78, N 3, p.360-373.
  2. 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.
  3. 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.
  4. Distraction of cycles in the foliations to analytic curves, Math. Sbornik, 1972, v.67, N 1, p.58-66.
  5. Foliations by analytic curves, Math. Sbornik, . 1972, v.88 N 4, p.558-577.
  6. Algebraic nonsolvability and almost algebraic solvability of the center-focus problem., Funct. Anal. Appl., 1972, v.6, N 3, p. 30-37.
  7. On the problems of rectification and cycle formation, Math. Sbornik, 1973, т.90, вып.2, с.184-195.
  8. 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.
  9. 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.
  10. On zeroes of special Abelian integrals in the real domain, Funct. Anal. and Pril. 1977, v.11, N 4, p.78-79.
  11. Multiplicity of limit cycles occurring under the perturbation of the Hamiltonian equations of the class $P_2/Q_1$ in the real and complex plane, Trudy sem. im. I.G.Petrovskogo, v.3, 1978, p. 29-40.
  12. 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.
  13. Global and local aspects of the theory of complex diffe- rential equations. Proceedings of International Congress of Mathematicians. Helsinki, 1978, p.821-826.
  14. (with Piartli) Zero type neighborhoods of embedded complex tori, Trudy sem. im. I.G.Petrovskogo, 1979, v. 5, p.85-95.
  15. (with Piartli) Materialization of Poincare resonances and divergence of normalizing series, Trudy sem. im. I.G.Petrovskogo, 1981, v.7, p.3-49.
  16. (with Piartli) Materialization of Poincare resonances and divergence of normalizing series for polynomial differential equations, Trudy sem. im. I.G.Petrovskogo, 1982, v 8, с.111-127.
  17. (with Chetaev) On the dimension of attractors of some dissipative systems, Appl. Math. Mech., 1982, v.46, N 3, p.374-381.
  18. 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.
  19. Positive type embeddings of elliptic curves to complex surfaces, Trudy MMO, 1982, v.46, p. 37-67.
  20. (with Elizarov) Remarks on orbital analytic classification of germs of vector fields, Math. Sbornik, 1983, v. 121, N 3 p.111-126.
  21. On the dimension of attractors of k-contracting evolutionary systems in infinite dimensional spaces, Vestnik MGU, ser. math., 1983, N 3, p. 52 - 59.
  22. 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.
  23. 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.
  24. 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.
  25. (with Arnold) Ordinary differential equations. In Encyclopedia of Mathematical Sciences, v 1, Moscow 1985, Springer 1986.
  26. (with Arnold, Afraimovich, Shil'nikov) Bifurcation theory. In Encyclopedia of Mathematical Sciences, v 5, Moscow 1986, Springer 1994.
  27. Separatrix bilaterals for planar vector fields, Vestnik MGU, ser. Math., 1986, N 4, p.25-31.
  28. Algebraically and analytically solvable local problems in theory of ordinary differential equations, Trudy sem. im. I.G.Petrovskogo, 1987, v 12, p. 118-136.
  29. (with Khovanskii) Galois groups, Stokes operators and Ramis theorem, Funct. Anal. and Appl., 1990, v.24, N 3, p.31-42.
  30. Finiteness theorems for limit cycles, Russian Math. Surveys, 1990, v.45, N 2, p.143-200.
  31. Finiteness theorem for limit cycles. Proceedings of International Congress of Mathematicians, Kyoto, 1990, v.11, p.1259-1270.
  32. Stability of the equilibrium points in hamiltonian systems with two degrees of freedom. Publication de l'Institut de Recherche Mathematique Avancee, 1990, 437, 11p.
  33. Finiteness theorems for limit cycles. Amer. Math. Soc., Transl. vol.94, 1991, 288 p.
  34. The concept of minimal attractors and maximal attractors of partial differential equations of the Kuramoto-Sivashinski type. Chaos 1, 1991, N2, p.168-173.
  35. (with Yakovenko) Smooth normal forms for local families of diffeomorphisms and vector fields, Russian Math. Surveys, 1991, v.46, N 1, p.3-39.
  36. Relaxation fast linear oscillations, Russian Math. Surveys, 1991, v.46, N 2, p.217-218.
  37. 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.
  38. editor of: Nonlinear Stokes Phenomena, series "Advances in Soviet Mathematics", v.14, Amer. Math. Soc., 1993.
  39. Nonlinear Stokes Phenomena, Nonlinear Stokes Phenomena, series ''Advances in Soviet Mathematics``, v.14, Amer. Math. Soc., 1993, 287 p.
  40. (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, in ''Nonlinear Stokes Phenomena``, 1993, Amer. Math. Soc., Advances in Soviet Mathematics, v14,p.57-106.
  41. (with Yakovenko) Nonlinear Stokes Phenomena in smooth classification problems, in ''Nonlinear Stokes Phenomena``, 1993, Amer. Math. Soc., Advances in Soviet Mathematics, v14, p.235-287.
  42. (with Yakovenko) Finite cyclicity of elementary polycycles. C.R.Acad.Sci., Paris, Serie 1, 316, 1993, p.1081-1086.
  43. Normal forms for local families and nonlocal bifurcations. Complex analytic methods in dynamical systems, Asterisque, 1994, 222, p.233-258.
  44. (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.
  45. (with Yakovenko) Counting real zeros of function satis- fying linear differential equations, p14, Journal of Differential Equations, 1996.
  46. (with Yakovenko) Double exponential estimate for the number of real zeros of complete Abelian Integral, Invenciones Matematicae, 1995, 25, 673-695.
  47. (with Arkhipov A.M.) Jump of energy from low harmoniks to the high ones in the multidimensional Kuramoto-Sivashinski equation, Selecta Mathematica formerly Sovietica, 1994, 13, 183 -196.
  48. Editor (with Yakovenko) of the book: Conerning Hilbert 16th problem, AMS, 1995, 219 pp.
  49. (with Yakovenko) Finite cyclicity of elementary polycycles, in book [48], pp. 21--96.
  50. Editor, Differential equations with real and complex time, collection of papers, proceedings of the Steklov Instisute, v. 213, 1996.
  51. Nonlinear Riemann--Hilbert problem, in book [50], pp. 6--29.
  52. (with Gorodetski) Minimal and strange attractors, International Journal of Bifurcation and Chaos, 1996, v. 6, N 6, 1177--1183.
  53. 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, pp.127-149.
  54. (with Li Weigu), Nonlocal Bifurcations, a Monograph, published by AMS, ser. Mathematical surveys and Monographs, 1998, vol.66.
  55. Covering manifolds for analytic families of leaves of foliations by analitic curves, Topological Methods in Nonlinear Analysis, 1998, v.11, 361-373.
  56. (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.
  57. (with Kaloshin) Bifurcation of planar and spatial polycycles: Arnold's program and its development, to appear.
  58. (with Saprykina) Embedding theorems for local families and oscilatory slow--fast systems, to appear.
  59. (with Gorodetski) Some new robust properties of invariant sets and attractors of dynamical systems, to appear.

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