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82:", 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
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Christiane Rousseau: Normal Forms, Bifurcations and Finiteness Problems in Differential Equations, Proceedings of a NATO seminar, Montreal, 2002, Kluwer, 2004
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Finiteness theorems for limit cycles, American
Mathematical Society Translations, 1991 (also published in Russian Mathematical Surveys, 45, 1990, 143–200)
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Ilyashenko, Yu (2000). "Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions".
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and persistence of heteroclinic intersections, Inventiones
Mathematicae, vol. 161, 2005, pp. 45–89
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Phenomena, Advances in Soviet Mathematics 14, AMS 1993
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His research deals with, among other things, what he calls the "infinitesimal
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independently proved the same result, and an earlier attempted proof by
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Selected topics in differential equations with real and complex time
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94:(in 1923) was shown to be defective by Ilyashenko in the 1970s.
284:"Yulij Ilyashenko, Mathematics Department, Cornell University"
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447:Academic staff of the Higher School of Economics
133:, Mathematical Surveys and Monographs, AMS 1998
313:"Centennial history of Hilbert´s 16th problem"
36:) is a Russian mathematician, specializing in
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452:Fellows of the American Mathematical Society
55:his Russian candidate degree (Ph.D.) under
32:(Юлий Сергеевич Ильяшенко, 4 November 1943,
138:Lectures on analytic differential equations
113:. In 2017 he was elected a Fellow of the
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348:Finiteness theorems for limit cycles
107:Finiteness theorems for limit cycles
145:Concerning the Hilbert 16th Problem
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97:He was an Invited Speaker of the
51:Ilyashenko received in 1969 from
16:Russian mathematician (born 1943)
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69:Independent University of Moscow
367:10.1090/S0273-0979-1993-00329-X
427:Moscow State University alumni
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354:Bull. Amer. Math. Soc. (N.S.)
330:10.1090/S0273-0979-02-00946-1
272:Mathematics Genealogy Project
115:American Mathematical Society
80:Hilbert's sixteenth problem
71:. He became a professor at
30:Yulij Sergeevich Ilyashenko
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437:Cornell University faculty
202:10.1088/0951-7715/13/4/319
143:as editor with Yakovenko:
249:10.1007/s00222-004-0418-8
67:, and also taught at the
344:Chicone, Carmen (1993).
311:Ilyashenko, Yu. (2002).
165:with Anton Gorodetski:
156:article by Ilyashenko:
53:Moscow State University
417:Russian mathematicians
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105:and in 1990 with talk
42:differential equations
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412:Soviet mathematicians
350:by Yu. S. Ilyashenko"
288:/www.math.cornell.edu
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236:{\displaystyle C^{2}}
131:Nonlocal Bifurcations
121:Selected publications
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393:at Wikimedia Commons
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317:Bulletin of the AMS
194:2000Nonli..13.1337I
136:with S. Yakovenko:
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175:10.1007/BF02465190
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346:"Review of
188:(4): 1337.
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88:Jean Écalle
406:Categories
397:mathnet.ru
255:References
147:, AMS 1995
140:, AMS 2007
46:foliations
210:250887845
160:, 317–354
103:Helsinki
84:cochains
293:Jul 30,
270:at the
190:Bibcode
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206:S2CID
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