Manchester Geometry Seminar
1999/2000
Special session. Second talk
Thursday, 4 May.
Room M12, Maths Tower, UMIST. 4.30 p.m.
Designing Efficient Liapounov Functions
Sir Peter Swinnerton-Dyer (University of Cambridge)
hpfs100@newton.cam.ac.uk
Let dxi/dt = fi(x1,¼,xn) for 1 £ i £ n be a
system of first order ordinary differential equations in R. A
function V(x1,¼,xn) is called a Liapounov function for
the system if
satisfies W < 0 whenever V ³ 0. Liapounov's theorem in its
simplest form states that if V is a Liapounov function then
(subject to some abuse of language in respect of behaviour at
infinity) every trajectory eventually enters the set {V £ 0}
and never thereafter leaves it.
The construction of efficient Liapounov functions is currently a
hit-and-miss affair. This seminar is a contribution towards
making the process more systematic.