Woensdag 27 februari 2008
Spreker: 
Onno van Gaans (Universiteit Leiden)

Titel: 
Periods of nonexpansive maps on finite dimensional normed spaces

Tijd: 
11:00  12:00

Plaats: 
HG00.062

Vanaf kwart voor 11 is er koffie en thee in de
binnenstraat
(voor de zaal).
Abstract
If
A is a square matrix of size
n with positive entries and
column sums at most 1, then successive application of
A to a vector
x yields a sequence of vectors, which `converges' to a periodic sequence.
The only periods that can occur are the periods of the permutations.
Such a matrix
A is nonexpansive (contractive) with respect to the 1norm
(sum norm). If the positivity is dropped, the periods can be twice as large.
We will discuss a class of norms on the
ndimensional real vector space
such that the orbits of any (nonlinear) nonexpansive map
f with
f(0)=0 converge to periodic sequences and such that the only possible
periods are orders or 2 times orders of permutations on
n symbols.
The analysis relies on an asymptotic decomposition into nonexpansive projections
and isometries on their ranges, and techniques of the isometric theory of
Banach spaces are used.
The lecture is intended for a general mathematical audience including
students.