List of publications
- Regular polygones in En, Vestnik MGU, ser. mat.
1962, no 8, p. 18-24.
- 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.
- 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.
- Multivalued functions on commutative normed rings, Vestnik
MGU, ser. mat., 1969, no. 5, p. 8-11.
- Nonalgebricity of the set of differential equations with
the rational right hand side having multiple limit cycles, Math,
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.
- Algebraic nonsolvability and almost algebraic solvability
of the center-focus problem., Funct. Anal. Appl., 1972, v.6,
N 3, p. 30-37.
- Foliations by analytic curves, Math. Sbornik, . 1972, v.88
N 4, p.558-577.
- On the problems of rectification and cycle formation, Math.
Sbornik, 1973, vol.90, no.2, p.184-195.
- Nondegenerate B-groups, Docl. Acad. Nauk SSSR, tom 208
(1973), no 3, 207-209.
- (with Khovanskii) Galois theory for Fuchsian systems of
differential equations with small coefficients, Preprint of the
applied mathematics, no 117, 1974, Moscow.
- 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,
- 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 zeros 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 P2/Q1 in
the real and complex plane, Trudy sem. im. I.G.Petrovskogo,
v.3, 1978, p. 29-40.
- 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,
- Global and local aspects of the theory of complex diffe-
rential equations. Proceedings of International Congress of
Mathematicians. Helsinki, 1978, p.821-826.
- 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.
- (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.
- In the normal forms theory under breaking of A.D.Brjuno
conditions divergence is a rool and convergence is an exception,
ser. mat., 1981, no. 5, p. 10-16.
- (with Piartli) Materialization of Poincare resonances
and divergence of normalizing series for polynomial differential
Trudy sem. im. I.G.Petrovskogo, 1982, v 8, p.111-127.
- (with Chetaev) On the dimension of attractors of some
dissipative systems, Appl. Math. Mech., 1982, v.46, N 3, p.374-381.
- Positive type embeddings of elliptic curves to complex
surfaces, Trudy MMO, 1982, v.46, p. 37-67.
- Weakly contracting systems and attractors of Galiorkin
approximations of the Navier-Stokes equations on the two-torus,
Mech. Surveys, 1982, v.5, N 1, p.31-63, transl. in Selecta
Math. Sov., v. 11 N 3, p. 203-239.
- Singular points and limit cycles of differential equations
in the real and complex plane, Preprint NIVTS AN SSSR, Pushchino,
1982, 38 p.
- (with Piartli) A polynomial vector field with singular
points of Poincaré type only, Funct. Anal. Appl., 1983,
v.17, N.4, p.84-85.
- (with Elizarov) Remarks on orbital analytic classification
of germs of vector fields, Math. Sbornik, 1983, v. 121, N 3
- 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
nonHausdorff Riemann surfaces. In Lecture Notes in Math; 1060,
- Dulac's memoir "On limit cycles" and related topics of
the theory of differential equations, Russian Math. Surveys,
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,
- A criterion of steepness for analytic functions, Russian
Math. Surveys, 1986, v.41, N.1, p.193-194.
- 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.
1987, v 12, p. 118-136.
- Singular points of vector fields (sceintific commentary),
in the book: I.G.Petrovskii, Selected papers, Moskow, Nauka,
- Limit cycles in real and complex planes (sceintific commentary),
in the book: I.G.Petrovskii, Selected papers, Moskow, Nauka,
- (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.
- 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 theorem for limit cycles. Proceedings of International
Congress of Mathematicians, Kyoto, 1990, v.11, p.1259-1270.
- 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.
- (with Yakovenko) Smooth normal forms for local families
of diffeomorphisms and vector fields, Russian Math. Surveys,
v.46, N 1, p.3-39.
- Relaxation fast linear oscillations, Russian Math. Surveys,
1991, v.46, N 2, p.217-218.
- The concept of minimal attractors and maximal attractors
of partial differential equations of the Kuramoto-Sivashinski
type. Chaos 1, 1991, N2, p.168-173.
- Global analysis of the phase portrait for the Kuramoto-
Sivashinski equation. Journal of dynamics and Dif. Equations.,
N 4, p. 585-615.
- Local dynamics and nonlocal bifurcations, in the book:
Bifurcations and periodic orbits of vector fields (Montreal,
PQ, 1992), 279-319,
- Editor of: Nonlinear Stokes Phenomena, series "Advances
in Soviet Mathematics", v.14, Amer. Math. Soc., 1993, 287 p.
- Nonlinear Stokes Phenomena, p. 1-55, in the book .
- (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 .
- (with Yakovenko) Nonlinear Stokes Phenomena in smooth
classification problems, p.235-287, in the book .
- (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
Math. Physics v.2 n 3, 275 -315.
- Editor (with Yakovenko) of: Conerning Hilbert 16th problem,
AMS, 1995, 219 pp.
- (with Yakovenko) Concerning Hilbert sixteenth problem,
p. 1-20, in the book .
- (with Yakovenko) Finite cyclicity of elementary polycycles,
in the book , pp. 21-96.
- (with Yakovenko ) Double exponential estimate for the
number of real zeros of complete Abelian Integral, Invenciones
1995, 25, 673-695.
- (with Kotova) Smale's horseshoe. Mathematical footwear
that left an imprint, Quantum, 1995, vol. 5, no 5, 13-18.
- (with Yakovenko ) Counting real zeros of function satisfying
linear differential equations, Journal of Differential Equations,
vol. 126. no 1, 1996, p. 87-105.
- (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.
- Limit cycles and nonlinear Stokes phenomena, p. 7-23,
in the book: The Stokes phenomenon and Hilbert's 16th problem,
- Editor of: Differential equations with real and complex
time, collection of papers, proceedings of the Steklov Instisute,
- The nonlinear Riemann-Hilbert problem, in the book ,
- (with Piartli) Rational differential equations with a
nonfree monodromy group at infinity, in the book , pp. 50-67.
- (with Shcherbakov) On skew cylinders and simultaneous
uniformization, in the book , p. 104-114.
- (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, p.127-149.
- (with Anosov, Aranson, Arnold, Bronstein, Grines) Ordinary
differential equations and smooth dynamical systems, Springer,
1997, 233 p.
- (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
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, in: Proccedings of the
Arnoldfest, Fields Institute Communications v.24, 1999, 241-271.
- (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.
- (with Gorodetski) Some new robust properties of invariant
sets and attractors of dynamical systems, Funct. Anal. Appl.,
1999, v. 33, n 2, 16-32.
- (with Li Weigu), Nonlocal Bifurcations, a Monograph, Russian
translation, edited, MCCME, Che-Ro, 1999.
- Hilbert type numbers for Abel equations, growth and zeroes
of holomorphic functions, Nonlinearity, v. 13, 2000, 1337-1342.
- (with A. Gorodetski) Some properties of skew products
over a horseshoe and solenoid, Procedings of the Steklov Institute,
v 231, 2000, 96-118.
- (with F.Dumortier and C.Rousseau) Normal forms near a
saddle-node and applications to finite cyclicity of graphics,
ETDS, v 22, 2002,
- (with J.Guckenheimer) The duck and the devil: canards
on the staircase, Moscow Mathematical Journal, v 1, no 1, 2001,
- (with A.Panov), Some upper estimates of the number of
limit cycles of planar vector fields with applications to Lienard
Moscow Mathematical Journal, v 1, no 4, 2001, 583-599
- Centennial history of Hilbert's 16th problem, Bull AMS,
v 39, no 3, 2002, 301-354
- (with V. Moldavskis) Morse-Smale diffeomorphisms of a
circle and moduli of elliptic curves, Moscow Mathematical Journal,
no 2, 2003, pp 1-10
- (with G. Buzzard and S, Hruska), Kupka-Smale theorem for
polynomial automorphisms of \Bbb C2 and persistence
of heteroclinic intersections, to appear
- Selected topics in differential equations with real and
complex time, in book "Normal forms, bifurcations and finiteness
problems in differential equations," Kluwer, to appear
- (with P. Hamke and S. Tabachnikov) Bringing Eastern European
Mathematical Traditions to North American Students, Notices
of the AMS, November 2003.