Applied Mathematics and Computation SeminarDiscrete Harmonic Functions and DynamicsProfessor Renato Feres, Washington University, St. Louis
The theory of dynamical systems is, very broadly, about
the study of actions of groups or semigroups of transformations
of a space X. For example, flows and iterations of invertible maps are
examples of actions of R and Z, respectively, and problems from diverse areas
of mathematics have lead to dynamics with more general types
of groups, such as SL(2,R) which will figure prominently
in this talk. Given a dynamical system with group G and space X I will focus
on Markov chains on X derived from random walks on G and
the associated space of harmonic functions on X. I will discuss a
dynamical version
of Liouville's theorem about bounded harmonic functions being constant, show
an interesting example of infinite dimensional chaotic system and fantasize
about what a dynamical Dirichlet problem might mean in this context.
Refreshments at 3:45
4:00pm–5:00pm, Tuesday, October 6, 2009 in LGRT 1634
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