Research Focus
-
Dynamical systems describing evolutionary processes in the world aroundus
-
Topology, Lie groups theory, theory of automorphicfunctions and so on
-
Understand thechaotic behavior of deterministic systems, and, in particular, to explainthe hydrodynamical turbulence
- New properties of dynamical systems that persist under small perturbations
-
Hilbert 16th problem
-
Applymethods of multidimensional complex analysis and theory of Riemann surfacesto the study of real polynomial differential equations
Publications
- Finiteness Theorems for Limit Cycles, AMS, Transl. 94,1991, 288 pp.
- Editor of Nonlinear Stokes Phenomena, Advances in Soviet Mathematics14, AMS, 1993, 287 pp.
- Editor (with Yakovenko) of Concerning Hilbert's 16th Problem,AMS, 1995, 219 pp.
- Minimal and strange attractors (with Gorodetski), Int'l J.Bifurcation and Chaos 6 no. 6 (1996), 1177–1183.
- Nonlocal Bifurcations (with Li Weigu), Mathematical Surveysand Monographs 66, AMS, 1999.
- Some new robust properties of invariant sets and attractors ofdynamical systems (with Gorodetski), Funct. Anal. Appl. 33no. 2 (1999), 16–32.
- Some properties of skew products over a horseshoe and solenoid(with A. Gorodetski), Proceedings of the Steklov Institute 231(2000), 96–118.
- Some upper estimates of the number of limit cycles of planar vectorfields with applications to Lienard equation (with A. Panov), MoscowMathematical Journal 1 no. 4 (2001), 583–599.
- Centennial history of Hilbert's 16th problem, Bull. AMS 39no. 3 (2002), 301–354.
- Editor (with C. Rousseau) of Normal Forms, Bifurcations and FinitenessProblems in Differential Equations, Proceedings of a NATO seminar,Montreal, 2002, Kluwer, 2004.
- Selected topics in differential equations with real and complextime; in Normal Forms, Bifurcations and Finiteness Problems in DifferentialEquations, Kluwer, 2004, pp. 317–354.
- Kupka-Smale theorem for polynomial automorphisms of C^2and persistence of heteroclinic intersections (with G. BuzzardandS. Hruska), Invent. Math. 161 (2005), 45–89.
- Non-removable zero Lyapunov exponents (with A. Gorodetski,V. Kleptsyn, M. Nalski), Functional Analysis and Appl. 39 no.1 (2005).
- Lectures on analytic differential equations (with S. Yakovenko),book in preparation.
