# Jerusalem Mathematics Colloquium

Thursday, 4th March 2004, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Professor Yosef Yomdin

(Weizmann)

"Closed trajectories of plane systems of ODE's, Moments, Compositions,
Iterated Integrals, and Algebraic Geometry"

** Abstract: **
A system of ordinary differential equations on the plane is
said to have a center at one of its singular points if all its
trajectories around this point are closed. It is a classical problem to
give explicit necessary and sufficient conditions for a system to have a
center (Center-Focus problem). Another closely related question is to
count isolated closed trajectories of a plane system (second part of
Hilbert's 16-th problem).

Recently in both these problems new connections have been found with some
questions in classical analysis and algebra. In particular, this concerns
the vanishing problem of certain moment-like expressions and of iterated
integrals on one side, and the structure of the composition factorization
of analytic functions on the other.

We present an overview of some recent developments in this direction.

Light refreshments will be served in the faculty lounge at 3:30.

List of talks, 2003-04

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List of talks, 2001-02

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List of talks, 1998-99

List of talks, 1997-98