July Sergeyevich Ilyashenko

July Sergejewitsch Ilyashenko ( Russian Юлий Сергеевич Ильяшенко , English transcription Yulij S. Ilyashenko ; born November 4, 1943 in Moscow ) is a Russian mathematician who deals with dynamic systems, differential equations and scrolling in complexes.

Ilyashenko received his doctorate in 1969 with Yevgeny Michailowitsch Landis at Lomonossow University . He was a professor at Lomonosov University, was at the Steklow Institute and is a professor at Cornell University . He also taught at the Independent University of Moscow.

Among other things, he deals with what he calls the infinitesimal 16th Hilbert problem : what can be done about the number and position of the limit cycles of a planar polynomial plane vector field (i.e. solutions of a real polynomial differential equation, components of degree n)? The problem is unsolved. Ilyashenko used new techniques of complex analysis (such as the method of functional co-chains, functional cochains). He proved that real plane polynomial vector fields only have a finite number of limit cycles. This was also shown independently by Jean Écalle, and an earlier attempt at proof by Henri Dulac (1923) was recognized by Ilyashenko as flawed in the 1970s.

He was invited speaker at the International Mathematicians Congress 1990 in Kyoto ( Finiteness Theorems for limit cycles ). He is a fellow of the American Mathematical Society .

Fonts

• Finiteness theorems for limit cycles, American Mathematical Society Translations, 1991 (and article of the same name Russian Mathematical Surveys, 45, 1990, 143-200)
• with Li Weigu: Nonlocal Bifurcations, Mathematical Surveys and Monographs, AMS 1998
• with S. Yakovenko: Lectures on analytic differential equations, AMS 2007
• Editor with Yakovenko: Concerning Hilbert's 16th problem, AMS 1995
• Editors: Nonlinear Stokes Phenomena, Advances in Soviet Mathematics 14, AMS 1993
• Editor with Christiane Rousseau: Normal Forms, Bifurcations and Finiteness Problems in Differential Equations, Proceedings of a NATO seminar, Montreal, 2002, Kluwer, 2004
  • therein by Iljashenko: Selected topics in differential equations with real and complex time, 317-354
• with G. Buzzard, S. Hruska: Kupka-Smale theorem for polynomial automorphisms of and persistence of heteroclinic intersections, Inventiones Mathematicae, Volume 161, 2005, pp. 45-89 ${\displaystyle C^{2}}$
• with Gorodetski Some new robust properties of invariant sets and attractors of dynamical systems , Functional Analysis and Applications, 33, No. 2, 1999, pp. 16-32.

Web links

• Homepage in Cornell
• mathnet.ru

Individual evidence

1. ↑ July Sergejewitsch Ilyashenko in the Mathematics Genealogy Project (English)
2. ↑ Ilyashenko Centennial history of Hilbert's 16 trouble , Bulletin AMS, 39, 2002, 301-354