Документ взят из кэша поисковой машины. Адрес
оригинального документа
: http://www.mccme.ru/ium/~yulijs/
Дата изменения: Mon Nov 10 15:11:09 2003
Дата индексирования: Tue Oct 2 01:03:22 2012
Кодировка: koi8-r
|
Юлий Сергеевич Ильяшенко,
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:
- Functional analysis and its applications (Nauka, Moscow)
- Dynamical and control systems (Plenum Press, New York and London)
- Ergodic theory and dynamical systems (Cambridge Univ. Press, UK)
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:
- Analytic theory of differential equations,
- Qualitative theory of differential equations (two years course),
- Bifurcation theory (local and nonlocal bifurcations),
- Selected topics in differential equations,
- Selected topics in complex analysis,
- Evolutionary systems and their attractors,
- Complex analysis, Cornell 1996,
- Dynamical systems, Cornell, 1996, 97,
- Measure theory and Lebesgue integration, Cornell 97.
The courses were mostly given several times and permanently modified.
For undergraduate students:
- Ordinary differential equations (modification of Arnold's course
with relations to complex analysis inserted).
PhD theses made under advisorship of Yu. Ilyashenko
- B.Muller, Local genericity of the density property for some classes
of equations in $CP^2$ and $C^3$, 1974;
- S.Voronin, Some problems of normal forms theory, 1983;
- A.Shcherbakov, Noncommutative groups of germs $(C,0) \to (C,0)$
and generic properties of differential equations in the complex
projective plane, 1983;
- P.Elizarov, Some questions of local theory of analytic differential
equations, 1986;
- N.Medvedeva, Stability problem for planar monodromic fixed points, 1988;
- S.Trifonov, Divergence of Dulac's series and desingularization in the
families of differential equations, 1991;
- L.Ortiz-Bobadilla, Topology of linear foliations in the
complex space, 1991;
- A.Glutsuk, Uniformization of leaves of one-dimensional complex foliations,
1996.
Participation in international congresses and conferences
- International Congress of Mathematicians, Helsinki, 1978,
45minute invited talk ''Global and local aspects of the
theory of complex differential equations`` in the section of
ordinary differential equations;
- International Congress of Mathematicians, 1990, 45-minute
invited talk ''Finiteness theorems for limit cycles``
in the section of ordinary differential equations;
- Equadiff, Barcelona, 1991, Plenary lecture "Finiteness theorems for limit
cycles and Hilbert-Arnold problem;
One or two-hour addresses in the conferences
- Periodic orbits and their bifurcations, Lumini, 1989,
- Resurgent functions, Paris, 1990,
- Dynamical systems, Nagoya, 1990,
- Dynamics days, Berlin, 1991,
- Colloque de Geometrie, Strasburg, 1991,
- Complex analytic methods in dynamical systems, Rio de Janeiro, 1992,
- Dynamical systems, Trieste, 1992,
- Geometrical colloquium, Moscow, 1993,
- Kolmogorov memorial conference, StPetersburg, 1993,
- Dynamical systems, Rio de Janeiro, 1993,
- Maryland-Penn State conference in Dynamical systems, College Park, 1994,
- Dynamical systems, Stony Brook, 1994,
- Dynamical systems, Moskow, 1994,
Member of the Organizing Committee for the last conference.
- International Congress in Dynamical systems, Montevideo, 1995,
- Ergodic Theory and Dynamical Systems (subject, not title), Jerusalem,
May 1995
- Dynamical Systems, Trieste, May 1995,
- The Stokes Phenomenon and Hilbert's 16th Problem, Groningen, June 1995,
- Geometrie complex et Systemes dynamique, Paris, July 1995,
- Dynamical Systems and Limit cycles
(subject, not title), Lumini, September 1995,
- Symposium on Dynamical Systems (subject, not title), Delft September 1995,
- Workshop on Dynamical Systems, Warsow, October 1995,
- Annual Meeteing of AMS, Orlando, January 1995,
- Contemporary problems in the Theory of dynamical systems,
Nigniy Novgorod, July 1996,
- 20th Congress of A.M.A.S.E.S., Urbino, September 1996,
- Iterates of maps, Urbino, September 1996,
- Contemporary problems in matematics, Samarkand, October 1996,
- Symposium on Planar vector fields, Leida, November 1996,
- Conference on Dynamical systems, Taejon, Korea, Fabruary 1997,
- International Congress in Dynamical systems, Guernavaca, Mexico, June 97,
- Arnoldfest (The conference in honour of V.I.Arnold's 60th
birthday),
Toronto, Canada, June 97,
- International Conference in Dynamical systems, Rio de
Janeiro, Brasil, August 97.
- Conference on Polynomial vector fields, Lumini, France, October 97,
- Conference: Multiple time-scaled dynamical systems,
Minneapolis, USA,October 97.
Courses in international workshops and schools
- Local dynamics, 5 lectures in Nice, 1990,
- Finiteness theorems for limit cycles, 5 lectures in Guanahuato, Mexico, 1991,
- Analytic theory of differential equations, 14 lectures in Trieste, 1991, 1992.
- Local dynamics and nonlocal bifurcations, 5 lectures in Montreal, 1992,
- Analytic theory of differential equations, new course, 12 lectures in Mexico,
and Guanajuato 1993,
- Nonlinear Stokes Phenomena, new course, 12 lectures in Mexico, 1995,
- Normal forms and Nonlocal bifurcations, 11 lectures in
Mexico and Guanajuato, 1996,
- Normal forms, limit cycles, desingulariation and bifurcations,
9 lectures, Toronto, January 1997.
Principal scientific achievements
- 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].
- Investigation of generic properties of polynomial vector fields
in the complex plane (talk in the ICM-1978) [12], [13], [44].
- Solvability of local problems of ODE:
- algebraic unsolvability of the center focus problem [6],
- analytic unsolvability of the Liapunov stability problem [8],
- general investigation of algebraically and analytically
solvable problems of local dynamics [28]
- Geometric theorems on divergence of normalizing series and
related topics in complex analysis [14],[15],[16],[19].
- 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].
- Nonlinear Stokes Phenomena: advisorship of the investigations
of Voronin, Elizarov, Shcherbakov, summarized in [38], including
[39], [40], [41].
- 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].
- 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
- 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.
- 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.
- 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.
- Distraction of cycles in the foliations to analytic curves,
Math. Sbornik, 1972, v.67, N 1, p.58-66.
- Foliations by analytic curves, Math. Sbornik, .
1972, v.88 N 4, p.558-577.
- Algebraic nonsolvability and almost algebraic solvability of the
center-focus problem., Funct. Anal. Appl., 1972, v.6, N 3, p. 30-37.
- On the problems of rectification and cycle formation, Math. Sbornik,
1973, т.90, вып.2, с.184-195.
- 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.
- 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.
- On zeroes of special Abelian integrals in the real domain,
Funct. Anal. and Pril. 1977, v.11, N 4, p.78-79.
- 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.
- 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.
- Global and local aspects of the theory of complex diffe-
rential equations. Proceedings of International Congress of Mathematicians.
Helsinki, 1978, p.821-826.
- (with Piartli) Zero type neighborhoods of embedded complex tori,
Trudy sem. im. I.G.Petrovskogo, 1979, v. 5, p.85-95.
- (with Piartli) Materialization of Poincare resonances and divergence
of normalizing series, Trudy sem. im. I.G.Petrovskogo, 1981, v.7, p.3-49.
- (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.
- (with Chetaev) On the dimension of attractors of some dissipative systems,
Appl. Math. Mech., 1982, v.46, N 3, p.374-381.
- 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.
- Positive type embeddings of elliptic curves to complex surfaces,
Trudy MMO, 1982, v.46, p. 37-67.
- (with Elizarov) Remarks on orbital analytic classification of germs
of vector fields, Math. Sbornik, 1983, v. 121, N 3 p.111-126.
- On the dimension of attractors of k-contracting evolutionary systems
in infinite dimensional spaces, Vestnik MGU, ser. math.,
1983, N 3, p. 52 - 59.
- 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.
- 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.
- 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.
- (with Arnold) Ordinary differential equations. In Encyclopedia of
Mathematical Sciences, v 1, Moscow 1985, Springer 1986.
- (with Arnold, Afraimovich, Shil'nikov) Bifurcation theory. In
Encyclopedia of Mathematical Sciences, v 5, Moscow 1986, Springer 1994.
- Separatrix bilaterals for planar vector fields, Vestnik MGU, ser. Math.,
1986, N 4, p.25-31.
- Algebraically and analytically solvable local problems in theory of
ordinary differential equations, Trudy sem. im. I.G.Petrovskogo,
1987, v 12, p. 118-136.
- (with Khovanskii) Galois groups, Stokes operators and Ramis theorem,
Funct. Anal. and Appl., 1990, v.24, N 3, p.31-42.
- Finiteness theorems for limit cycles, Russian Math. Surveys, 1990, v.45,
N 2, p.143-200.
- Finiteness theorem for limit cycles. Proceedings of
International Congress of Mathematicians, Kyoto, 1990, v.11, p.1259-1270.
- Stability of the equilibrium points in hamiltonian systems
with two degrees of freedom. Publication de l'Institut de Recherche
Mathematique Avancee, 1990, 437, 11p.
- Finiteness theorems for limit cycles. Amer. Math. Soc.,
Transl. vol.94, 1991, 288 p.
- The concept of minimal attractors and maximal attractors
of partial differential equations of the Kuramoto-Sivashinski type.
Chaos 1, 1991, N2, p.168-173.
- (with Yakovenko) Smooth normal forms for local families of
diffeomorphisms and vector fields, Russian Math. Surveys,
1991, v.46, N 1, p.3-39.
- Relaxation fast linear oscillations, Russian Math. Surveys,
1991, v.46, N 2, p.217-218.
- 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.
- editor of: Nonlinear Stokes Phenomena, series "Advances in
Soviet Mathematics", v.14, Amer. Math. Soc., 1993.
- Nonlinear Stokes Phenomena, Nonlinear Stokes Phenomena, series
''Advances in Soviet Mathematics``, v.14, Amer. Math. Soc., 1993, 287 p.
- (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.
- (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.
- (with Yakovenko) Finite cyclicity of elementary polycycles.
C.R.Acad.Sci., Paris, Serie 1, 316, 1993, p.1081-1086.
- Normal forms for local families and nonlocal bifurcations.
Complex analytic methods in dynamical systems, Asterisque, 1994, 222,
p.233-258.
- (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.
- (with Yakovenko) Counting real zeros of function satis-
fying linear differential equations, p14,
Journal of Differential Equations, 1996.
- (with Yakovenko) Double exponential estimate for the
number of real zeros of complete Abelian Integral,
Invenciones Matematicae, 1995, 25, 673-695.
- (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.
- Editor (with Yakovenko) of the book: Conerning Hilbert
16th problem, AMS, 1995, 219 pp.
- (with Yakovenko) Finite cyclicity of elementary
polycycles, in book [48], pp. 21--96.
- Editor, Differential equations with real and complex
time, collection of papers, proceedings of the Steklov Instisute,
v. 213, 1996.
- Nonlinear Riemann--Hilbert problem, in book [50],
pp. 6--29.
- (with Gorodetski) Minimal and strange attractors,
International Journal of Bifurcation and Chaos, 1996, v. 6,
N 6, 1177--1183.
- 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.
- (with Li Weigu), Nonlocal Bifurcations, a Monograph,
published by AMS, ser. Mathematical surveys and Monographs, 1998,
vol.66.
- Covering manifolds for analytic families of leaves of foliations by
analitic curves, Topological Methods in Nonlinear Analysis, 1998, v.11,
361-373.
- (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.
- (with Kaloshin) Bifurcation of planar and spatial polycycles: Arnold's
program and its development, to appear.
- (with Saprykina) Embedding theorems for local families and oscilatory
slow--fast systems, to appear.
- (with Gorodetski) Some new robust properties of invariant sets and
attractors of dynamical systems, to appear.