Yulij Sergeevich Ilyashenko (Юлий Сергеевич Ильяшенко, 4 November 1943, Moscow) is a Russian mathematician, specializing in dynamical systems, differential equations, and complex foliations.
Ilyashenko received in 1969 from Moscow State University his Russian candidate degree (Ph.D.) under Evgenii Landis.[1] Ilyashenko was a professor at Moscow State University, an academic at Steklov Institute, and also taught at the Independent University of Moscow. He became a professor at Cornell University.[2]
His research deals with, among other things, what he calls the "infinitesimal Hilbert's sixteenth problem", 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 cochains).[3] 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.[3]
He was an Invited Speaker of the ICM in 1978 at Helsinki and in 1990 with talk Finiteness theorems for limit cycles at Kyoto. In 2017 he was elected a Fellow of the American Mathematical Society.
