A centennial history of Hilbert's 16th problem
(second part)


Yulij S. Ilyashenko

Cornell University

Northeastern University

Thursday, November 16, 2000


Talk at 4:30 p.m. in 509 Lake Hall

Tea at 4:00 p.m. in 544 Nightingale Hall


Abstract:   The second part of the 16th problem appeared to be one of the most difficult on Hilbert's list. Smale included it in his list of the main problems for the forthcoming century. In the expiring century the problem had a long and dramatic history. In the last 20 years the interest in the problem has substantially grown, and some progress was achieved. Several associated problems about ``Hilbert type numbers'' were stated and partially solved.

One can mention in this context ``Finiteness theorems for limit cycles'' proved independently by Ecalle and the speaker; ``Hilbert-Arnold problem'' partly solved by Yakovenko and the speaker; ``Infinitesimal Hilbert problem'' about zeros of Abelian integrals, studied by Varchenko, Khovanski, Petrov, Yakovenko, D. Novikov and others; upper bounds for the number of limit cycles for Abel and Lienerd equations, recently obtained.

A sketch of the history and these achievements will be the subject of the talk.


Here are some directions to Northeastern University. Lake Hall and Nightingale Hall can be best accessed from the entrance on the corner of Greenleaf Street and Leon Street. The two halls are connected, with no well-defined boundary in between. In particular, 509 Lake Hall is on the same corridor as 544 Nightingale Hall.

There is free parking available for people coming to the colloquium at Northeastern's visitor parking. The entrance is from Columbus Avenue, right next to the parking garage.

Home Web page:  Alexandru I. Suciu  Comments to:
Created: October 21, 2000    URL: