Infinitesimal Hilbert's 16th problem |
Abstract:
The second part of Hilbert's 16th problem is about the maximal
possible number of isolated ovals (also called limit cycles) on the
phase portraits of planar polynomial vector fields. The general
question still remains open. Only various local or semilocal versions
of this problem seem to be accessible, every time with great efforts.
In 2000 Yu. Ilyashenko gave a lecture "Centennial History of Hilbert's
16th Problem" at this colloquium (the extended version appeared in
Bull. AMS), focusing on the (semi)local study of limit cycles near
separatrix polygons which implies, among other things, finiteness of
their number for each particular polynomial vector field. This was the
main achievement of the theory by that time. |
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 (Rennaisance Garage). The entrance is from Columbus Avenue. If coming by car, you should park there and take the parking talon. After the lecture, you may pick up the payment coupon from Andrei Zelevinsky. |
Web page: Alexandru I. Suciu | Comments to: alexsuciu@neu.edu | |
Posted:: January 15, 2009 | URL: http://www.math.neu.edu/bhmn/yakovenko09.html |