Yulij Sergeevich Ilyashenko (Юлий Сергеевич Ильяшенко, 4 November 1943,

Moscow Moscow ( , US chiefly ; rus, links=no, Москва, r=Moskva, p=mɐskˈva, a=Москва.ogg) is the capital and largest city of Russia. The city stands on the Moskva River in Central Russia, with a population estimated at 13.0 million ...

) is a Russian mathematician, specializing in dynamical systems, differential equations, and complex

foliation In mathematics (differential geometry), a foliation is an equivalence relation on an ''n''-manifold, the equivalence classes being connected, injectively immersed submanifolds, all of the same dimension ''p'', modeled on the decomposition of ...

s. Ilyashenko received in 1969 from

Moscow State University M. V. Lomonosov Moscow State University (MSU; russian: Московский государственный университет имени М. В. Ломоносова) is a public research university in Moscow, Russia and the most prestigious ...

his Russian candidate degree (Ph.D.) under

Evgenii Landis Evgenii Mikhailovich Landis (russian: Евге́ний Миха́йлович Ла́ндис, ''Yevgeny Mikhaylovich Landis''; 6 October 1921 – 12 December 1997) was a Soviet mathematician who worked mainly on partial differential equations. ...

. Ilyashenko was a professor at Moscow State University, an academic at Steklov Institute, and also taught at the

Independent University of Moscow The Independent University of Moscow (IUM) (russian: Независимый Московский Университет (НМУ)) is an educational organisation with rather informal status located in Moscow, Russia. It was founded in 1991 by a gro ...

. He became a professor at

Cornell University Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...

. His research deals with, among other things, what he calls the "infinitesimal

Hilbert's sixteenth problem Hilbert's 16th problem was posed by David Hilbert at the Paris conference of the International Congress of Mathematicians in 1900, as part of his list of 23 problems in mathematics. The original problem was posed as the ''Problem of the topolo ...

", which asks what one can say about the number and location of the boundary cycles of planar polynomial vector fields. The problem is not yet completely solved. Ilyashenko attacked the problem using new techniques of complex analysis (such as functional

cochain In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is included in the kernel of t ...

s). He proved that planar polynomial vector fields have only finitely many limit cycles. Jean Écalle independently proved the same result, and an earlier attempted proof by Henri Dulac (in 1923) was shown to be defective by Ilyashenko in the 1970s. He was an Invited Speaker of the ICM in 1978 at

Helsinki Helsinki ( or ; ; sv, Helsingfors, ) is the Capital city, capital, primate city, primate, and List of cities and towns in Finland, most populous city of Finland. Located on the shore of the Gulf of Finland, it is the seat of the region of U ...

and in 1990 with talk ''Finiteness theorems for limit cycles'' at

Kyoto Kyoto (; Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in Japan. Located in the Kansai region on the island of Honshu, Kyoto forms a part of the Keihanshin metropolitan area along with Osaka and Kobe. , the ci ...

. In 2017 he was elected a Fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

Selected publications

*Finiteness theorems for limit cycles, American Mathematical Society Translations, 1991 (also published in Russian Mathematical Surveys, 45, 1990, 143–200) *with Weigu Li
Nonlocal Bifurcations
Mathematical Surveys and Monographs, AMS 1998 *with S. Yakovenko
Lectures on analytic differential equations
AMS 2007 *as editor with Yakovenko
Concerning the Hilbert 16th Problem
AMS 1995 *as editor: Nonlinear Stokes Phenomena, Advances in Soviet Mathematics 14, AMS 1993 *as editor with Christiane Rousseau: Normal Forms, Bifurcations and Finiteness Problems in Differential Equations, Proceedings of a NATO seminar, Montreal, 2002, Kluwer, 2004 **article by Ilyashenko
Selected topics in differential equations with real and complex time
317–354 *with Anton Gorodetski: ''Certain new robust properties of invariant sets and attractors of dynamical systems'', Functional Analysis and Applications, vol. 33, no. 2, 1999, pp. 16–32. * *with G. Buzzard and S. Hruska: Kupka-Smale theorem for polynomial automorphisms of

C^2

and persistence of heteroclinic intersections, Inventiones Mathematicae, vol. 161, 2005, pp. 45–89

References

External links

*
mathnet.ru
{{DEFAULTSORT:Ilyashenko, Yulij Sergeevich Soviet mathematicians Russian mathematicians 21st-century American mathematicians Moscow State University alumni Academic staff of Moscow State University Cornell University faculty Academic staff of the Independent University of Moscow Academic staff of the Higher School of Economics Fellows of the American Mathematical Society 1943 births Living people