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

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

) is a Russian mathematician, specializing in

dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models ...

s, differential equations, and complex

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

s. Ilyashenko received in 1969 from

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

his Russian candidate degree (Ph.D.) under

Evgenii Landis Evgenii Mikhailovich Landis (, ''Yevgeny Mikhaylovich Landis''; 6 October 1921 – 12 December 1997) was a Soviet mathematician who worked mainly on partial differential equations. Life Landis was born in Kharkiv, Ukrainian SSR, Soviet Union. H ...

and

Vladimir Arnold Vladimir Igorevich Arnold (or Arnol'd; , ; 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. He is best known for the Kolmogorov–Arnold–Moser theorem regarding the stability of integrable systems, and contributed to s ...

. Ilyashenko was a professor at Moscow State University, an academic at

Steklov Institute Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Ste ...

, and also taught at the

Independent University of Moscow The Independent University of Moscow (IUM) () is an educational organisation with rather informal status located in Moscow, Russia. It was founded in 1991 by a group of Russian mathematicians that included Vladimir Arnold (chairman) and Sergei No ...

. He became a professor at

Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...

. 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 topology ...

", 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 Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

(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 contained in the kernel o ...

s). He proved that planar polynomial vector fields have only finitely many limit cycles.

Jean Écalle Jean Écalle (born 1947) is a French mathematician, specializing in dynamic systems, perturbation theory, and analysis. Écalle received, in 1974 from the University of Paris-Saclay in Orsay, a doctorate under the supervision of Hubert Delange wit ...

independently proved the same result, and an earlier attempted proof by

Henri Dulac Henri Claudius Rosarius Dulac (3 October 1870, Fayence – 2 September 1955, Fayence) was a French mathematician. Life Born in Fayence, France, Dulac graduated from École Polytechnique (Paris, class of 1892) and obtained a Doctorate in Math ...

(in 1923) was shown to be defective by Ilyashenko in the 1970s. He was an Invited Speaker of the

ICM ICM may refer to: Organizations * Irish Church Missions, an Anglican mission * Institut du Cerveau, the Paris Brain Institute, a research center * Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw * Interna ...

in 1978 at

Helsinki Helsinki () is the Capital city, capital and most populous List of cities and towns in Finland, city in Finland. It is on the shore of the Gulf of Finland and is the seat of southern Finland's Uusimaa region. About people live in the municipali ...

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

Kyoto Kyoto ( or ; Japanese language, Japanese: , ''Kyōto'' ), officially , is the capital city of Kyoto Prefecture in the Kansai region of Japan's largest and most populous island of Honshu. , the city had a population of 1.46 million, making it t ...

. 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 ''Uspekhi Matematicheskikh Nauk'' () is a Russian mathematical journal, published by the Russian Academy of Sciences and Moscow Mathematical Society and translated into English as ''Russian Mathematical Surveys''. ''Uspekhi Matematicheskikh Nauk' ...

, 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 ''Inventiones Mathematicae'' is a mathematical journal published monthly by Springer Science+Business Media. It was established in 1966 and is regarded as one of the most prestigious mathematics journals in the world. The current (2023) managing ...

, 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

Selected publications

References

See also

External links